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The design of a cascaded 800 MeV normal conducting C.W. race track microtron
NUCLEAR INSTRUMENTS
AND
METHODS
THE DESIGN OF A CASCADED C.W.
I38 (I976) I - I 2 ;
800 M e V N O R M A L
© NORTH-HOLLAND
PUBLISHING
CO.
CONDUCTING
RACE TRACK MICROTRON*
H. HERMINGHAUS, A. FEDER, K. H. KAISER, W. MANZ and H. v. d. SCHMITT lnstitut fiir Kernphysik der Johannes Gutenberg-Universitiit,
Mainz, IV. Germany
Received 9 July 1976 A c.w. electron accelerator of 820 MeV maximum output energy at 100/2A beam current is proposed to make possible a large variety of coincidence experiments with medium energy electrons and photons as a future possibility of new, interesting experiments. It consists of a preaccelerator and 3 cascaded race track microtrons using normal conducting rf structures. The design of this accelerator, based on detailed computational investigations of its beam dynamics and some experimental studies, is communicated and partly discussed in this paper.
1. Introduction
2. Basic design considerations
F r o m several groups at M a i n z University the wish c a m e up to have an electron b e a m o f a b o u t 600 MeV, a duty cycle close to 100% a n d at least some tens o f m i c r o a m p s intensity. W i t h such a b e a m a large variety o f very interesting new experiments could be made1). To achieve this goal the possibility had been investigated to recycle the existing 300 M e V linac once a n d to feed the beam into a pulse stretcher ring ( U R M E L ) 2). This investigation revealed, however, that this kind o f realisation w o u l d have been surprisingly expensive - mainly due to the necessity o f m a j o r changes in the existing buildings - and yet a considerable risk with respect to b e a m quality w o u l d have h a d to be t a k e n into account. Therefore, since s u m m e r '74 the construction o f a c.w. race t r a c k m i c r o t r o n ( R T M ) , called M A M I t , has been considered as an alternative and has been a d o p t e d as the m o r e attractive solution. Since 600 M e V seemed r a t h e r low for m a n y o f the planned experiments the design objective for the m a x i m u m energy was increased to 820 M e V at a m a x i m u m c.w. beam current o f 100/~A. F o l l o w i n g the p a p e r o f Wiik a n d W i l s o n 3) designs o f high d u t y cycle R T M s have been published by several authors4-8). There has been, however, to our knowledge, no p r o p o s a l up to now t h a t c o n s e q u e n t l y c o m b i n e s the a d v a n t a g e s o f c.w. service (highest d u t y cycle, no transient b e a m l o a d i n g p r o b l e m s , ease o f accurate control) with the reliable, well k n o w n technology o f r o o m t e m p e r a t u r e rf structures. W e feel, however, t h a t this c o m b i n a t i o n might result in a quite attractive design, as we h o p e to show in the following.
The design o f a R T M (see fig. 1) is basically governed by the resonance c o n d i t i o n
* This work has been supported in part by the Deutsche Forschungsgemeinschaft, Bad Godesberg. t Mainz Mikrotron.
2.096 A T = v 2 B ,
(1)
where A T i s the energy gain in the linac section in MeV, 2 the rf v a c u u m wavelength in cm a n d B the magnetic field strength in the m a i n magnets in T. v is the n u m b e r o f wavelengths by which the orbit circumference is increased from one turn to the next. Clearly, if a r o o m t e m p e r a t u r e linac structure is to be o p e r a t e d as a c.w. accelerator there is a strong d e m a n d for low A T for the sake o f rf p o w e r e c o n o m y a n d cooling problems. The increase in pathlength per turn, v2, c a n n o t be m a d e deliberately small because the orbit spacing d which is given by d = v;oln
(2)
should be at least a b o u t 4 cm, to allow the return paths to be guided t h r o u g h individual b e a m pipes a n d to be steered by individual steering coils - a feature which is a special benefit o f the R T M a m o n g cycling machine3 and which should n o t be sacrificed. The magnetic field, B, c a n n o t be m a d e deliberately small for e c o n o m i c reasons, since m a g n e t costs grow
Fig. 1. Scheme of a RTM.
2
H. HERMINGHAUS et al.
rapidly with the diameter of the pole faces. Even with B lying in the most economical region between 1.0 and 1.6T, magnet costs are dominant for a R T M for several hundred MeV. For 820 MeV a field strength of about 1.5T renders a good compromise between magnet and rf expense, leading to ATe9 MeV per turn according to eq. (1), if in eq. (2) d ~ 4 cm is obeyed. Eq. (2) leaves the choice v = l , 2 ~ 1 2 cm or v = 2 , 2 ~ 6 cm, etc. The choice of v = 1 gives the best stability for the longitudinal particle motion and allows the least stringent tolerances for the magnetic field homogeneity. Moreover, there are powerful c.w. klystrons available around 2-- 12 cm and 4 cm but none at 6 cm. Since v > 2 would result in severe stability and tolerance problems and 2 < 6 cm would give impractically small beam apertures of the rf structure there is a clear decision for v = 1, 2 ~ 12 cm. The energy gain of a linac, A T, can be expressed as A T = cos q5 ~/(rPL),
(3)
where q5 is the phase of the particles with respect to the crest of the rf wave, r the effective shunt impedance, P the total rf power dissipation in the linac and L the total length of the linac. With A T and r being given a compromise must be found between P and L, since large L makes the beam dynamics more difficult and raises construction cost, and large P makes cooling of the rf structure difficult and raises the operation costs. A reasonable compromise in our case is to dissipate about 20 k W / m ; inserting q5=20 ° and r = 4 0 Mf2/m (see below) we get the desired 9 MeV by dissipating 200 kW of rf power within about 11 m of rf structure. Thus, as compared with pulsed RTMs or RTMs using a superconducting accelerator, the room temperature c.w. R T M has to operate at a relatively high frequency with v = 1, low accelerating field and relatively large spacing between magnets. These choices lead immediately to a major difficulty of this kind of machine: injection problems which are important for other R T M s are even more severe in our case mainly for three reasons: l) Small wavelength and low gradient in the rf structure and large spacing of the magnets call for high injection energy to enable coherent acceleration. 2) Large spacing of the magnets implies relatively weak focusing, resulting in a large beam diameter especially at low energies. 3) A large ratio of magnet spacing to bending radius makes the compensation of the fringe field defocusing rather critical, especially with respect to
chromatic errors and third order aberrations in beam optics (see appendix). To overcome these difficulties relatively high injection energy must be chosen which, however, is rather expensive to achieve in c.w. operation in a conventional manner. Generally, it is seen that injection energy may be lower for the smaller size of the RTM. This suggests the use of a small R T M as an economic injector of a larger one. Point 3 together with the demands for reasonable magnet size and a reasonably low number of recycling loops limit the ratio of output to input energy of a single R T M stage to about 10. (For a pulsed or superconducting R T M the same rule applies if the first linactraversal is considered to be part of the injection,) At electron energies of about 2 MeV or less, phase slip due to low particle velocity becomes so dominant that a R T M does not offer a practical solution any more. Therefore, preacceleration to 2-3 MeV has to be provided by means of a c.w. linac or a dc accelerator. Hence there are three R T M stages necessary to bridge the range from 2 to 820 MeV. Thereby the energy gain ratio of each stage is still less than 10 and this in principle offers the opportunity to accomplish transverse focusing by a quadrupole triplet on the linac axis. (Theoretically, with respect to beam diameter, the decrease of focusing strength with increasing energy is compensated by pseudo-damping.) As compared with focusing by individual quadrupoles on the return paths this method would be very economical and it avoids the otherwise strong coupling between longitudinal and horizontal particle oscillations. Furthermore it offers the advantage of defining the linac axis automatically as the optical axis for all revolutions. This could lead to considerable simplification in adjustment, monitoring and operation of the system. This latter advantage applies also in comparison with split pole focusing which would, moreover, lead to a more complicated magnet construction. A closer look at this kind of focusing shows, however, that it leads to very stringent requirements with respect to field homogeneity in the bending magnets, at least in stages 2 and 3. For these stages we therefore based our design on the less convenient use of quadrupoles on the individual return paths. In stage 1, however, focusing on the linac axis is possible, whereas focusing on the return paths would lead to a severe reduction in acceptance especially in this stage (see below). It should be emphasized that the particular difficulties of our design are at least partly compensated by certain simplifying features: As compared with pulsed RTMs, there are no transient phenomena to care about in our case. Especially we do not have the problem of transient
C. W. R A C E T R A C K
beam loading, and the problem of stability of rf sources may easily be solved by simple control loops, leading to very simple klystron power supplies. Further, at a given average current, c.w. service gives the lowest possible beam emittance which, in turn, helps to meet the more stringent requirements of our machine in this respect. A special advantage of cascading is the fact that the experience gained in constructing and operating a small stage may be used for the construction of the next bigger one, thus reducing the risk for the entire machine considerably. Further we consider it an essential advantage that the two first stages which are relatively inexpensive could provide a c.w. beam of about 100MeV, suitable for a variety of interesting coincidence experiments of the types (e, e'n) and (e,e'7). This by itself could justify the construction of the first two stages. An earlier design of the machine has been given in ref. 9.
3. Optimisation of design parameters and beam optics of M A M I The design is based on the use of the T H O M S O N CSF type T H 2075 c.w. klystron* which gives 50 kW rf power at an efficiency close to 60%. Within its frequency range of (2450_+25)MHz we chose for some practical reasons 2 = 12.240 cm (f=2449.3 MHz). The distance between return paths then becomes 3.896 cm. For optimisation of stages 1 and 2 essentially the following demands had to be taken into account: a) In order to get a 100 MeV beam in a first construction step at the least possible rf expense stages 1 and 2 should be driven by one common klystron. b) Injection energy of stage I should be as low as possible, but high enough to allow coherent acceleration in a straighforward manner. c) The number of turns in stage 1 should be kept sufficiently low so that beam optics are not too much affected by space charge effects. d) Care must be taken that beam optics are not too much affected by higher order aberrations of the fringe field optics of the bending magnets whose influence is approximately proportional to L / R 2 ( L = m a g n e t spacing, R = b e n d i n g radius, see appendix). To evaluate the beam dynamics data of all stages two entirely different computational methods have been used in parallel: 1) An
interactive program called " M E L L Y
* A special version of TH 2054.
7"
MICROTRON
3
running on the medium size computer (CDC 1700) of our laboratory. This program calculates particle trajectories in a similar manner as the program " T R A N S P O R T " lo) does. However, a special matrix algorithm is used which offers the possibility to carry out calculations up to any order; thereby, only non-vanishing matrix elements are stored. In our case, third order proved to be sufficient to take into account all couplings of any significance between different phase space coordinates, a sine-shaped travelling wave in the accelerator and the spherical aberration in the vertical optics of the reverse field lenses of the bending magnets in an analytical approximation (see appendix). This program is very fast and, in connection with some special computer periphery, it is possible to vary several parameters currently by means of potentiometer inputs observing the resultant trajectories on a C R T screen, much as with an analog computer. This p r o g r a m was extremely useful for quick optimisation of parameters. 2) A program called " M I T R A C E " which consists essentially of the " R A Y T R A C E " - p r o g r a m of Enge and Kowalski supplied by a code for tracing particles through an accelerator section. In this program beam optics in the bending magnets were computed using the fringe field shape as measured in a model magnet. Its shape was not optimised for small spheric aberration which gives some margin of safety in this respect. This program has been used to evaluate the phase space transformations through the R T M s by computing many particle trajectories and to investigate the influence of some small errors in field homogeneity on beam optics. It should be mentioned that the fringe field optics of the model magnet have been measured experimentally by deflecting a 200 keV electron beam of well defined, small emittance by 180 °. The condition for infinite vertical focal length and the magnitude of the spherical aberration have been determined and were found to be in good agreement with the M I T R A C E results. In the following we will present the results of numerous computations which lead in a sense to a close to optimum design of beam guidance. It should be kept in mind, however, that so far only two types of focusing systems have been investigated: one using a focusing lens on the linac axis only and the other using alternate singuletts on the return paths only, with constant focal length for all turns. In both cases fringe field optics were adjusted to nearly infinite focal
4
H. H E R M I N G H A U S et al.
TABLE 1
Parameters of MAMI. Stage
1
General Input energy (MeV) Output energy (MeV) Number of turns Distance between magnets (m) (eft. field boundary)
2.11 14.0 21
Magnet Field strength (T) system Radius of inner orbit (m) Radius of outer orbit (m) Gap width (cm) Pole face diameter (m) Magnet diameter (m) Weight (t) (one magnet) Rf system
Beam optics
Number of klystrons Accelerating field amplitude (MeV/m) Electrical length of accelerator (m) Dissipated power (kW) Beam power (kW) (100/IA) Energy gain of synchronous particle (MeV) Synchronous phase angle (deg) Focusing method
Focal length
Normalized input beam emittance ]ongit. (keV.deg) horiz. (moc m m .mrad) vert. (mocm m . m r a d ) Normalized output beam emittance longit. (keV.deg) horiz. (moc m m . r a d ) vert. (moc m m . r a d )
2
14.0 100 43
3
100 820 80
1.66
5.21
0.100 0.086 0.484 2 1.14 1.3 1.2
0.342 1.537 0.142 0.218 0.980 1.781 3 3 2.14 3.72 2.5 5.4 8.5 240 1
0.893 0.71 13.9 1.2 0.588 22
single focusing lens on linac
16 m at l0 MeV
11.83
6
0.512 4.06 26.3 8.6 2.00 16
0.936 10 216 72 9.00 16
quadrupole singlets on the return paths, alternately focusing and defocusing orbit circumference times -k/2
18 n 4.7n 4.5n
26 n 6.7n 6.9n
67n 16n 14n
18 n 4.7n 4.5n
39 n ll.3n 7.0n
105n 34n 16n
length23). In principle, of course, any combination of these methods could be tried and some of them might give better results. The major task of our investigation was, however, to show just o n e possibility that would give satisfactory results. The parameters thus obtained are compiled in table 1, a scaled scheme of the accelerator is shown in fig. 2.
The small gap width in stage 1 is chosen in order to get an accordingly small fringe field length, resulting in low longitudinal dispersion which helps to decrease the input energy. This argument is not crucial for the two other stages. So the gaps may be chosen larger there which helps to keep the more stringent tolerances with respect to field homogeneity. The parameters of the rf systems are calculated assuming an effective shunt impedance of about 40 MQ/m. This is rather low and leaves us some margins to fight multipactoring and cooling problems (see below). The large synchronous phase angle of 22 ° in stage 1 is especially useful in getting low minimum injection energy. A still larger value, however, would lead to a reduced stable phase area in longitudinal phase spaceal'lz), Moreover, we found by numerical calculation using the M E L L Y 7 code that even the 22 ° would lead to instability in stage 1 if transversal focusing were done by alternate singlets in the return paths. This instability appears as if the Q-value of the transverse oscillations were heavily reduced with increasing energy (though quadrupole field strength was chosen proportional to particle momentum), ending up in an integer resonance. The effect is the stronger the smaller the magnet distance and the larger the synchronous phase angle. The effect is amplitude dependent (reduction of bucket size) and it accordingly disappears if only first order transfer matrices are used for computation of the particle trajectories. This instability is also the reason that the synchronous phase angle in stages 2 and 3 is chosen relatively small since in these stages singlets in the return paths have to be used for focusing, for reasons discussed earlier. extraction
.....
~
. . . .
O.X.
guiding magnet 0
'
'
'
'
5rn
--e--
beam
monitor
Fig. 2. Scaled scheme of MAMI. The bumps in the last return paths of stages 1 and 2 serve for longitudinal beam matching.
C. W . R A C E
TRACK
The single focusing lens on the linac of stage 1 may consist of a pair of solenoid lenses, excited oppositely to each other to minimize beam rotation. The quadrupole singlets of stages 2 and 3 may be realized by means of thin copper coils with an outer iron shield. A transversal beam emittance of about 4.5 nmoc m m . r a d and a longitudinal one of 1 8 n d e g ' k e V has been assumed at the entrance of stage 1. This is ample for a beam intensity of 100/tA. In the first stage there is T-2110-(n-05).
588
[ keY ]
21
/.. 100 3
0 C - - : - b2
"50
1
-20
-15
-10
-5
10
15
20 koZ [ o]
Fig. 3. Longitudinal emittance areas in the midst o f the linac o f stage 1 for successive turns (n), T is the kinetic energy o f the electrons, 2110 keV is the kinetic energy o f the s y n c h r o n o u s electron entering stage 1 and 588 keV the energy gain for a relativistic electron passing t h r o u g h the linac at 22 ° (ko = co~c).
MICROTRON
5
practically no spread in phase space since the focusing method used prevents strong coupling between different phase space planes. Entering stage 2, however, some spread has been assumed as a margin for field inhomogeneity, misalignments and matching errors. During acceleration in stage 2 phase space areas are increased, mainly in longitudinal and horizontal phase space, due to coupling by the quadrupole singlets in the return paths. Entering stage 3 a further increase is assumed to allow for field errors, etc. The shapes of the different phase space areas at different locations in the accelerator are shown in figs. 3-6. These areas fill relatively small parts of the acceptance bucket. Their shape is, therefore, mostly rather closely elliptic. Taking into account some further margins of safety it is seen that the beam will leave stage 3 with a transversal emittance of about 3 x x 10 - z n m m ' m r a d at 820 MeV, total energy width being about Ap/p=2x 10 - 4 . AS has been estimated synchrotron radiation effects should not change these data significantly. It should be stressed that these design parameters are chosen to have some margins of safety in beam optics and that we considered it important the whole beam optics to be as straightforward and conservative as possible to ease operation of the machine. For these reasons, for instance, we refrained from using extra
x ' [ mrad ]
"\
/
/
AT [ k e Y ]
stage 2
-05
/
50
in I / / /
\
'\
-04
\
• 0.3
\ \
,. . . . .
.02
'\
'0.1L-"- ~ - . .
1
AT [ keY ]
x[cm]
stage 3
~
OU
'\
x
\
out'3
/
'\
'\ AI.[ o]
]
x-
\
//stage '\
/ \,
/
_/"
1..... 2 ..... 3 - -
_i
Fig. 4. Longitudinal emittance envelopes in the midst o f the linac o f stages 2 and 3 taking into account transversal emittance as shown in figs. 5 and 6.
Fig. 5. H o r i z o n t a l emittance envelopes in the midst o f the linac o f the three stages taking into account vertical and longitudinal emittances as s h o w n in figs. 3, 4 a n d 6 (in: first turn; out: last turn ref. to stages 1 and 3, last but one ref. to stage 2).
6
H. HERMINGHAUS et al.
orbits in the first stage for lower input energy and rather chose a somewhat less economic preaccelerator.
4. Preaccelerator The preaccelerator has to render a beam of 2.11 MeV, containing 100 pA in bunches of 2.4 ° in length and 33.0 keV energy width. As a first alternative we investigated a dc gun of several 100 keV followed by a few short rf accelerator sections with constant phase velocity each. We finally adopted the design shown in fig. 7 which would need about 25 kW of rf power13). The tilt of the phase space volume is correct to match the input admittance of stage l, taking into account the longitudinal dispersion of the injection path. It seems, however, that a Van de Graaff accelerator, equipped with a low power double drift buncher in the terminal would be much more convenient as a preaccelerator, especially with respect to the much less complicated beam dynamics involved. On the other hand it would be markedly more expensive.
intensity, bunch phase and transverse position of the beam with respect to the linac axis at each individual passage and it must be sufficiently sensitive to operate at a beam intensity of 100 pA and less. These requirements may be satisfied using rf resonance cavities as monitors and " m a r k i n g " the beam with short intensity bursts or blackouts. Successive passages may then be identified by the time at which the burst (or blackout) signal appears in the display. For initial optimisation for a run we plan to use a sequence of beam pulses of 12 ns duration - j u s t sufficient to resolve individual passages even in the first stage - at a repetition frequency of about 10 kHz. Thus, during the most critical phase of beam optimisation, the average beam power is too low to cause any harm
chopper, cov. / d.c.gun
1
To take advantage of the feature of individually guided beam loops an adequate monitoring and steering system is inevitable. This system, which will be described in the following, is shown schematically in fig. 8. The monitoring system must be able to determine
I 4BOkeV ~ 1 ~
1/'"
/'//" ,/
/
~--2AOm
beornchopped to 20degrees bunchlength
0.4 . . . . .
/CX ,kov
10¸
~*'2~z
-10"
L03
\
[02
in2 , "\~
out 1.._:_"0~"
in3 ,'
!
/
i
Fig. 7. T h e rf preaccelerator. (a) Scheme of preacceterator; ,Sw = normalized phase velocity. (b) Longitudinal o u t p u t emittance for i n p u t phase range o f 4-12 ° a n d i n p u t energy spread o f 4-1 keV; ko = o)/c.
/
!
/'
Jt
/
I
,/" /
[ "]
~--,.\
J
\,
2.11MeV
0,525m~ ,~T[keV]
l y'[ mrad ] 0,5
in
fl~ 0.978 _/
5. Monitoring and steering
/-
P,,v=Q.g26
./
stoge 1 - - - - . . . . . .
vett~~ hor....-~---J~
Ii n e ~ 7 ~
" rat.
3 Fig. 6. Vertical emittance envelopes in the midst o f the linac o f the three stages taking into account horizontal a n d longitudinal emittances as s h o w n in the figs. 3, 4 a n d 5 (in: first t u r n ; out: last t u r n ref. to stages 1 a n d 3; last but one ref. to stage 2).
int. phase
vert,
hoe
Fig. 8. Monitoring and steering system; D B M : double balanced mixer.
C.W. R A C E T R A C K
to components in case of misalignment. Then beam intensity between the pulses will be increased little by little, successively reoptimizing the operation parameters (essentially rf power and -phase). Finally, at beam intensities of more than half the maximum value, beam blackouts instead of bursts will be used of equal duration and repetition rate. If the dc component is suppressed in the display both burst and blackout mode give identical signals, except for the polarity. The voltage amplitude U o induced by a bunched beam traversing a properly tuned cavity is given by
d~-,'
z
~ J(t);
U
Uo e
,
where r = 2 Q/co is the attenuation time of the field in the cavity, Q its loaded Q-value and F=(VoT)2/W, where Vo is the voltage at the beam position, T the transit-time factor and W the stored energy in the cavity. J(t) is the dc component of the bunched beam intensity. Thus, there are essentially two possible modes of operating a cavity as a fast beam monitor: If r is large compared to the beam pulse duration rB, the above equation gives
it is not difficult to manufacture with sufficient accuracy to get excellent decoupling of the two degenerate modes. Further experiments using a pulsed 200 keV bunched beam of ll ns pulse length showed that the high Q mode operation works very well with the differentiating arrangement as shown in fig. 9. The low Q mode has not yet been tried. Of course, when operating such monitors in an accelerator, care must be taken to keep the high power rf from the cavities and to avoid disturbance from other noise sources. We are qu[te confident, however, to achieve this by inserting cutoff pipes of about l0 cm in length between monitor and linac and by mounting the DBM and a fast video preamplifier immediately at the cavity. Transverse steering will be done in the individual recycling paths as shown in fig. 8. The essential constraint in the construction of the steering elements is given by the small spacing between return paths of
or, after rf detection by a double balanced mixer (DBM) as a phase sensitive device, a s s u m i n g - 7 dB conversion loss and a 50 g2 video load, Uv being the video signal voltage:
tsv~/(5~F)fJdt
(high Q mode).
(4)
b
a
<
ver, lpos.
Iq
Isign.lpr °b_
/ ~[~
Uo F ~ J dt, U° ~ VAT-2
7
MICROTRON
/
',
17
i
II
x.
hot. pos. signalprobe
~f. ~ C H r ef. . . .
I
;added ( ' ~ 1 k.L,/
bH
,nve edJ
CRT I
/ / fe~d through termination M_M2 m cable 50 S2 Fig. 9. (a) rf b e a m position m o n i t o r with experimental setup for high Q m o d e operation. (b) Field pattern as induced by vertical (left) a n d horizontal (right) b e a m offset respectively.
If r is chosen small compared to rB, then Uv ~ ~/(5 Fz)
J
(low Q mode).
(5)
Both operation modes may give about the same video signal amplitude, namely about 5 mV at J = 100/~A, if a single pillbox cavity is used as an intensity and phase monitor. As a beam position monitor a cavity of square cross section may be used which is resonant in the TM210 mode in two directions rectangular to each other (see fig. 9). With such a cavity a video signal of the order of 0.2 mV/mm at 100 ~A is to be expected which is well above detector and preamplifier noise. If desired, the signal-to-noise ratio could be improved considerably by using a sampling technique and raising the prf to 100 kHz. Experiments with a model cavity showed that
k38.96 -~ I ~ I ~
.-~ (
~
.~ beam pipe
horizontal steering colts
.11 .41 ..4 I ~
J~d4
L
~-~\vertical
~ ~
/
"
~
'steering
.
bea.m .p©e t:/eam pipe omitted +horizontal steering coils omitted
coils
Fig. 10. Transverse b e a m steerer, consisting o f an array o f w i n d o w frame m a g n e t s (schematic view a n d cross section, all m e a s u r e s in m m ) .
8
H. H E R M I N G H A U S
3.9 cm only and the necessity o f negligible cross coupling between neighbouring elements. We could meet these requirements by a construction as shown in fig. 10. Measurements with a prototype of 16 cm in length on a 200 keV electron beam showed cross coupling from an excited cell to its next neighbour to be as low as 2 x 10 -3. F r o m there on the stray field decreases further from cell to cell by a factor of about 4 each. This prototype gave a deflecting field of 57 G at 5 A in the coils for horizontal deflection (which are the more critical ones). Thus, a steerer of about 50 cm in length is sufficient to do steering up to 4-1 mrad at 820 MeV. 6. Field errors
We do not see an equally simple method for longitudinal steering, i.e. rf phase correction on successive passages. Field errors o f _+3 x 10 -4 in SBds which will cause 4- 1 mrad deviation in horizontal beam direction m a y cause in the last orbits o f stage 3 a longitudinal shift of 0.7 cm, corresponding to about 20 ° in rf phase. This would be clearly too much if it would change stochastically from turn to turn. It is to be expected, however, that the changes between successive turns will be rather small. In this case one should rather speak of an adiabatic shift in resonant rf phase which would then a m o u n t to about 10 °. This should still be lowered by at least a factor 5 and the best way to do this is to make small field corrections in the region indicated in fig. 11. Experiments with a small model magnet showed that it is possible to make these corrections by locating small pieces of magnetic material in the Purcell-filter between pole piece and yoke. Referring again to transversal beam optics, calculations show that it would not be greatly affected by a smooth field gradient of 10 -4 cm 1. Some care should be taken, however, with respect to the second derivative o f the field and it can be estimated that, in order not to affect markedly the beam proFerties, the gap width
Fig. 11. Most effective region for longitudinal orbit correction.
et al.
should not change by more than 1 Ftm over a distance of typically 1.5 cm (it may change, however, by a larger a m o u n t over distances much shorter or larger than 1.5 cm). In stage 3 these tolerances would be even narrower by about an order o f magnitude if in this stage focusing were done by a single lens on the linac axis only. Referring to unwanted dc or ac magnetic fields, such as the earth's field or fields produced by currents in cables or ground loops, it is easily estimated that their influence on the beam is not dangerous and will be negligible if a thin magnetic shield is applied on the beam guides between the magnets and reasonable care is taken with respect to power cables and grounding. It is seen from the above discussion that much trouble can be avoided if the magnets can be operated always at essentially the same field strength in order to reproduce a field pattern, once optimized, within narrow limits from run to run. 7. Variable energy extraction
Mainly for the reason just mentioned we will change output energy essentially not by varying magnetic field strength (and rf field strength accordingly) but by extracting the beam from one of the inner orbits. The extraction scheme is shown in fig. 12. The return paths pipes within the energy variation range end up downstream in a c o m m o n vacuum c h a m b e r which protrudes by 2 m from the bending magnet. Just in front o f this chamber a special deflection steerer is put over the pipe from which the beam is to be extracted. It is excited to deflect the beam by 35 mrad inwards. The beam then leaves the accelerator in the way shown in fig. 12.
extraction chamber
/
..--------q\ / '[
['movable Jextraction ~-] magnet
\Lo28Testamlox. /35mrad
Fig. 12. Extraction scheme for variable output energy.
9
C.W. R A C E T R A C K M 1 C R O T R O N
The extraction steerer will be made of two easily separable halves and may quickly be clamped over another pipe if a change in output energy is desired. To interpolate between the discrete energies of successive orbits field strengths in deflecting magnets and rf section may be changed by small amounts: changes of -± 1.5% are sufficient to get any energy value down to 300 MeV. 8. Rf structures
Cooling capability and multipactoring are the two main restrictions by which an otherwise good accelerator structure could turn out to be unsuitable for c.w. operation at room temperature. At present we are considering three possible candidates: a) the iris-structure in the SLAC-design14), b) the side coupled structure in the L A M P F designlS.16), c) the jungle gym structure in the design as used at Cornel117.18). The iris structure in the S L A C design can be cooled very effectively because of its rather thick irises: a temperature drop across the iris of no more than about 10°C is to be expected at a power consumption of 20 kW/m. If the structure is designed as a constant gradient structure with small group velocity and an external feedback is used, an overall shunt impedance of about 50 Mf2/m is to be expected at our frequency. In this case, however, the sensitivity of the structure to thermal deformation is very high, so that the temperature at the circumference of the structure finally has to be held constant within a few tenths of a degree and tuning of the section would have to be done under design power operation. Fig. 13 and table 2 show as r ~.10 3
o
/
b
[cml 9.52
IIIIIIIIlllll
\ /
t 18.6kw
3.4 db
12.6 kW
c
950 9.48 120
2b 2a
/ ~40.8 ~'0
10 20 30 40 50 60 z[cm]
radius = 2.8 mm
Fig. 13. Design of the linac o f stage 1 using the iris structure. (a) Parameter variation along the axis, (b) resonant loop, (c) cross section, measures in m m ; cooling is done by 60 axial cooling pipes, formed by grooves 4 mm by 4 m m and an outer water jacket.
TABLE 2 Properties of the linac shown in fig. 13.
Total energy gain Dissipated power Electrical length Mode Beam load derivative Phase change along cold section Phase change along section due to temperature distribution under beam load conditions
0.634 cos 22 ° = 0.588 MeV 11.7 kW 61.2 cm (15 cavities)
2n/3 3.8 MI2 50 °
an example the design of the accelerator section of stage 1. It has been reported that multipactoring at the field levels of c.w. operation can be overcome if some technological precautions are observed19). The side coupled structure offers the highest shunt impedance among all competitors: 65 Mf2/m, if the EPA-structure is scaled to our frequency. Most of this virtue, however, is caused by its narrow aperture of 1.25 cm which might result in beam handling difficulties. But even if the shunt impedance has partly to be sacrificed in favor of a larger aperture there would still remain the advantage of simplicity in operation, without a feedback loop. Presumably temperature differences within this structure would be too high at our power levels unless cooling ducts were provided in the walls between cavities and near the nose cones2°). Little seems to be known about its behaviour with respect to multipactoring in the relevant range of 30 60 keV per cavity. The jungle gym structure has excellent cooling capability, its mechanical tolerances are not critical, it is easy to manufacture and - due to its odd geometry serious difficulties with multipactoring are most unlikely to occurl8). It needs, however, a recirculating loop with high circulating power and its shunt impedance is rather low - the value of 40-Mf2/m given in table I applies for this structure. Thus, for our application the jungle gym structure seems to be the safest, but least economic, choice. At present we are doing some model measurements on this structure. Table 3 gives a rough summary of the properties of the three structures under consideration. Beam break-up (BBU) has not yet been observed in microtrons, to the best of our knowledge. There is, however, an estimation formula by Wilson 21) and a closer investigation by Volodin22). The latter has shown that the Fresence of transverse focusing generally raises the starting current by a large factor. An estimation following ref. 22 shows that even in the
10
H. H E R M I N G H A U S et al.
TABLE 3 General comparison of the three kinds of linac structures under consideration. Structure
Iris (SLAC)
Side-coupled (EPA)
Jungle gym (Cornell)
Mode Group velocity Cooling Tolerances Power handling capability
2n/3 travelling wave 0.0060-0.0037 c good close medium
n/2 travelling wave 0.22 c good wide good
Shunt impedance Pumping Feeding Risk of multipactoring
good medium resonant loop medium
n standing wave 0.04 e difficult medium presumably good, with sophisticated cooling system excellent medium simple unknown
limit of vanishing transverse focusing there is no danger of beam break-up in stage 1. In stages 2 and 3, however, a shunt impedance for the break-up mode of just a few M ~ / m could be sufficient in this case to excite the instability (the estimation formula of ref. 20 gives a somewhat more optimistic result). On the other hand, in stages 2 and 3 there is rather strong focusing by the quadrupoles in the return paths, giving a Q of about 1/8 (Q is about 1/4 with respect to the magnetic period of 2 turns). This should suppress BBU by at least one order of magnitude. Since there are several possibilities left to lower the shunt impedance for the BBU mode of the section substantially we are quite confident that BBU could be overcome in all stages of M A M I .
9. Summary Our design of a room temperature c.w. electron accelerator of 820 MeV output energy leads to a cascade of three S-band race track microtrons with input energies of 2.11, 14 and 100 MeV respectively, fed by a small linac or a Van de Graaff as preaccelerator. In these considerations in general the spherical aberrations of the fringe field optics play a quite significant role. An analytical estimate for these aberrations is generally given in the appendix. Numerous computations of particle trajectories by the aid of two independent computer codes suggest to accomplish focusing at the first R T M by two oppositely excited solenoids on the linac, on the two other RTMs by alternating quadrupole singlets on the return paths. With reasonable margins of safety a beam of 100/~A within an emittance of 3× 1 0 - 2 n m m . m r a d and a relative energy spread of 2 × 10 -4 may be expected at 820 MeV. For lower energy the beam is extracted from one of the inner return paths by the aid of a small inward deflec-
poor excellent resonant loop of high gain low
tion. Monitoring will be done by three rf cavities on the linac axis of each RTM, short intensity bursts or blackouts of the beam serving for orbit identification. Model measurements have been done on some crucial components as bending magnets, beam monitors and special steering elements. Referring to rf structure, cooling capability and multipactoring at our relatively low field gradients are believed to be the main restrictions in our case. There are at present three candidates under consideration: iris structure, side coupled structure and jungle gym structure. A final decision between these requires measurements on short experimental sections under vacuum at full power. Some design studies have been done so far on the iris structure. In the near future special emphasis will be laid on these questions. At present a 50 kW c.w. rf source is being built and some measurements are done on the jungle gym structure. We would like to express our thanks to Prof. A. O. Hanson, Univ. of Illinois, for many informative discussions and his valuable suggestions on the major part of this paper. We would like to thank further the colleagues of our tab and of neighbouring institutes for leaving much operation time on their computers to us.
Appendix: Some
remarks on the reverse field optics
In the following expressions are briefly derived which allow to estimate the spherical aberrations in vertical direction, the dispersion and the coupling of vertical position to longitudinal position occurring during the passage of a beam through a Babic-Sedlacek fringe field23). Using the designations of fig. 14, the Lorentz force
C.W. RACE TRACK MICROTRON in vertical direction reads
Assuming that y remains essentially constant during the passage of the fringe field zone, eq. (6) m a y be written by the aid of eqs. (7) and (8) as
Fy = - evB z sin 0~, which gives
Y' = ~1 {Ylfl B=-Bdz-dlt(B'~zdzlokBo/o --
y,, _ -eB= sin mocfly COS2 (~'
2y3 f : ( B " ~ 2 d z + . . . } , 3 \Bo/
where the dashes mean derivation with respect to z. Using
-el
since--
Bydz,
---
m o c fly
and assuming c~ to be small enough that, for an estimation, cos2~ ~- 1, we get
=
Bz
By dz.
(6)
~ ( y , z ) = - y B + y 3 B " - y 5 -B(4) - + .... 120
(7)
1
_
m
~', 0y
.
B= = -- --c3~e.
c3=
~
L
(B/Bo) 2 dz -
(8)
m.__
-
(B/Bo)
dz ,
(10)
(,,,y --
ft
dz
3 R 2 ,Jo \ B o /
(11)
'
where y is the distance of the b e a m from the middle plane. This corresponds to a spherical aberration. It is seen from eq. (11) that in order to keep this aberration small B' should be distributed rather uniformly over the fringe zone. So the (fictitious) fringe field distributions shown in fig. 15, while all satisfying f0-1 = 0 , should be rather close to the o p t i m u m for small spherical aberrations. A m o n g the curves shown, 1 and 3 give aber-
B(z) pole face
R2
;o
and, if B(z) is chosen in such a way that)Co becomes infinite, the focal length f l for a b e a m off-axis is still finite and given by
,
where B = B ( z ) is the field in the middle plane ( y = 0 ) . Then
(9)
where z = 0 ... l denotes the fringe field zone, B o is the field inside the magnet and R the radius of curvature of the particle trajectory there. F r o m this it is seen that the focal length f o for particles near the middle plane is given by
fo Generally, a plain static field, symmetrical with respect to the (x, z)-plane, m a y be derived from a potential
By -
11
1 b =B,~'I/~.(~- ~1)
Bo
ac rive clamp y/x b z
...a-¢ Fig. 14. Definition of symbols and coordinates used in the appendix,
Fig. 15. Examples for close to optimum field distributions giving infinite vertical focal length.
12
H. HERMINGHAUS et al. o f the b e a m as a f u n c t i o n o f its vertical d i s p l a c e m e n t y in the fringe z o n e is c a l c u l a t e d a p p r o x i m a t e l y to be
r a t i o n s o f equal strength, lower t h a n 2, given by
Ax = y2/2R,
This is j u s t 3 times the error p r o d u c e d by a n ideally straight fringe field o f the s a m e l e n g t h w i t h o u t c o m p e n s a t i o n o f vertical defocusing. The field d i s t r i b u t i o n o f a m o d e l m a g n e t w h i c h was n o t o p t i m i s e d with respect to low a b e r r a t i o n s a n d was t h u s r a t h e r far f r o m the n e a r o p t i m u m d i s t r i b u t i o n s o f fig. 15 (I) gives, f o l l o w i n g M I T R A C E , a 1.32 times larger value. This d i s t r i b u t i o n has b e e n used t h r o u g h o u t the M 1 T R A C E c o m p u t a t i o n s . T h e l o n g i t u d i n a l disp e r s i o n s o f d i s t r i b u t i o n s 1 a n d 3 are o b t a i n e d by s t r a i g h t f o r w a r d rectification o f the trajectories. F o r a w h o l e 180 ° b e n d i n g m a g n e t the t r a j e c t o r y l e n g t h S is in case 1 : S = rrR + 21 [0.788675 + 0.002726 ( l / R ) 2 ] , in case 3 : S = ~R + 21 [ - 0.28868 + 0.07089 ( l / R ) 2 ] . (13) So b o t h d i s t r i b u t i o n s give a c o n t r i b u t i o n to longit u d i n a l d i s p e r s i o n o f the s a m e sign as a particle with e n e r g y d e p e n d e n t velocity does, b u t in case 1 this c o n t r i b u t i o n is m u c h smaller. So case 1 is to be preferred t h o u g h case 3 m a y have the a d v a n t a g e n o t to need a n active field c l a m p a n d to result in a s m a l l e r pole face area. C o m p a r i n g eqs. (12) a n d (13) it is seen t h a t m a k i n g the fringe field d e p t h l large m a y result in small spherical a b e r r a t i o n s in vertical b e a m optics, b u t l o n g i t u d i n a l l y the a d d i t i o n a l phase shift w h i c h is i n t r o d u c e d b y a n y fringe field at low b e n d i n g radii is increased a n d vice versa. By i n t e g r a t i n g -e x " -- - By(z, y), m o cfl~
u s i n g eqs. (7) a n d (8), the h o r i z o n t a l d i s p l a c e m e n t A x
(14)
which is i n d e p e n d e n t o f the f o r m o f the fringe field. This is i d e n t i c a l with the e x p r e s s i o n used in the " T R A N S P O R T " - p r o g r a m 1°) for n o r m a l fringe fields.
References i) Vorschlag zur Weiterentwicklung der physikalischen Arbeitsm6glichkeiten am Mainzer Elektronen-Linearbeschleuniger fiir den Zeitraum yon 1975 bis 1990, Institut for Kernphysik, Universit/it Mainz (24. Febr. 1975). 2) H. Herminghaus, Proc. 9th Int. Conf. on High energy accelerators, Stanford (1974). 3) B. H. Wiik and P. B. Wilson, Nucl. Instr. and Meth. 56 (1967) 197. 4) D. C. Sutton et al, IEEE Trans. Nucl. Sci. NS-16 (1969) 985. 5) j. M. Volkov et al., Proc. 7th Int. Conf. on High energy accelerators, Yerewan (1969). 6) D. Barbero et al., Proc. 8th Int. Conf. on High energy accelerators, Genf (1971). 7) R. E. Rand, IEEE Trans. Nucl. Sci. NS-20 (1973) 938. s) R. Alvinsson et al., Inst. of Physics, Lund University, Rep. LUSY 7501 (Jan. 1975). 9) A. Feder et al., Institut ftir Kernphysik, Universit~it Mainz, Int. Rep. KPH 2/1976 (Jan. 1976). lo) K. L. Brown, SLAC-Rep. Nr. 75 (July 1967). 11) G. Bathow and E. Freytag, DESY Report 69/29 (August 1969). 12) V. N. Melekhin, Soy. Phys. JETP 34 (1972) 702. 13) A. Feder, Inst. f. Kernphysik, Universit~it Mainz, Int. Rep. KPH 8/1976 (June 1976). 14) G. A. Loew et al., in The Stanford two mile accelerator (ed. R. B. Neal; Elsevier, New York, Amsterdam, 1968). 15) E. A. Knapp et al., Rev. Sci. Instr. 39 (1968) 979. 16) E. A. Knapp, IEEE Trans. Nucl. Sci. NS-16 (1969) 329. 17) M. Tigner, IEEE Trans. Nucl. Sci. NS-18 (1971) 249. is) j. L. Kirchgessner and M. Tigner, IEEE Trans. Nucl. Sci. NS-20 (1973) 928. 19) j. Haimson, private communication. 2o) E. A. Knapp, private communication. 21) p. B. Wilson, IEEE Trans. Nucl. Sci. NS-20 (1973) 1018. 22) V. A. Volodin and A. O. Hanson, IEEE Trans. Nucl. Sci. NS-22 (1975) 1194. z3) H. Babic and M. Sedlacek, Nucl. Instr. and Meth. 56 (1967) 170.
AND
METHODS
THE DESIGN OF A CASCADED C.W.
I38 (I976) I - I 2 ;
800 M e V N O R M A L
© NORTH-HOLLAND
PUBLISHING
CO.
CONDUCTING
RACE TRACK MICROTRON*
H. HERMINGHAUS, A. FEDER, K. H. KAISER, W. MANZ and H. v. d. SCHMITT lnstitut fiir Kernphysik der Johannes Gutenberg-Universitiit,
Mainz, IV. Germany
Received 9 July 1976 A c.w. electron accelerator of 820 MeV maximum output energy at 100/2A beam current is proposed to make possible a large variety of coincidence experiments with medium energy electrons and photons as a future possibility of new, interesting experiments. It consists of a preaccelerator and 3 cascaded race track microtrons using normal conducting rf structures. The design of this accelerator, based on detailed computational investigations of its beam dynamics and some experimental studies, is communicated and partly discussed in this paper.
1. Introduction
2. Basic design considerations
F r o m several groups at M a i n z University the wish c a m e up to have an electron b e a m o f a b o u t 600 MeV, a duty cycle close to 100% a n d at least some tens o f m i c r o a m p s intensity. W i t h such a b e a m a large variety o f very interesting new experiments could be made1). To achieve this goal the possibility had been investigated to recycle the existing 300 M e V linac once a n d to feed the beam into a pulse stretcher ring ( U R M E L ) 2). This investigation revealed, however, that this kind o f realisation w o u l d have been surprisingly expensive - mainly due to the necessity o f m a j o r changes in the existing buildings - and yet a considerable risk with respect to b e a m quality w o u l d have h a d to be t a k e n into account. Therefore, since s u m m e r '74 the construction o f a c.w. race t r a c k m i c r o t r o n ( R T M ) , called M A M I t , has been considered as an alternative and has been a d o p t e d as the m o r e attractive solution. Since 600 M e V seemed r a t h e r low for m a n y o f the planned experiments the design objective for the m a x i m u m energy was increased to 820 M e V at a m a x i m u m c.w. beam current o f 100/~A. F o l l o w i n g the p a p e r o f Wiik a n d W i l s o n 3) designs o f high d u t y cycle R T M s have been published by several authors4-8). There has been, however, to our knowledge, no p r o p o s a l up to now t h a t c o n s e q u e n t l y c o m b i n e s the a d v a n t a g e s o f c.w. service (highest d u t y cycle, no transient b e a m l o a d i n g p r o b l e m s , ease o f accurate control) with the reliable, well k n o w n technology o f r o o m t e m p e r a t u r e rf structures. W e feel, however, t h a t this c o m b i n a t i o n might result in a quite attractive design, as we h o p e to show in the following.
The design o f a R T M (see fig. 1) is basically governed by the resonance c o n d i t i o n
* This work has been supported in part by the Deutsche Forschungsgemeinschaft, Bad Godesberg. t Mainz Mikrotron.
2.096 A T = v 2 B ,
(1)
where A T i s the energy gain in the linac section in MeV, 2 the rf v a c u u m wavelength in cm a n d B the magnetic field strength in the m a i n magnets in T. v is the n u m b e r o f wavelengths by which the orbit circumference is increased from one turn to the next. Clearly, if a r o o m t e m p e r a t u r e linac structure is to be o p e r a t e d as a c.w. accelerator there is a strong d e m a n d for low A T for the sake o f rf p o w e r e c o n o m y a n d cooling problems. The increase in pathlength per turn, v2, c a n n o t be m a d e deliberately small because the orbit spacing d which is given by d = v;oln
(2)
should be at least a b o u t 4 cm, to allow the return paths to be guided t h r o u g h individual b e a m pipes a n d to be steered by individual steering coils - a feature which is a special benefit o f the R T M a m o n g cycling machine3 and which should n o t be sacrificed. The magnetic field, B, c a n n o t be m a d e deliberately small for e c o n o m i c reasons, since m a g n e t costs grow
Fig. 1. Scheme of a RTM.
2
H. HERMINGHAUS et al.
rapidly with the diameter of the pole faces. Even with B lying in the most economical region between 1.0 and 1.6T, magnet costs are dominant for a R T M for several hundred MeV. For 820 MeV a field strength of about 1.5T renders a good compromise between magnet and rf expense, leading to ATe9 MeV per turn according to eq. (1), if in eq. (2) d ~ 4 cm is obeyed. Eq. (2) leaves the choice v = l , 2 ~ 1 2 cm or v = 2 , 2 ~ 6 cm, etc. The choice of v = 1 gives the best stability for the longitudinal particle motion and allows the least stringent tolerances for the magnetic field homogeneity. Moreover, there are powerful c.w. klystrons available around 2-- 12 cm and 4 cm but none at 6 cm. Since v > 2 would result in severe stability and tolerance problems and 2 < 6 cm would give impractically small beam apertures of the rf structure there is a clear decision for v = 1, 2 ~ 12 cm. The energy gain of a linac, A T, can be expressed as A T = cos q5 ~/(rPL),
(3)
where q5 is the phase of the particles with respect to the crest of the rf wave, r the effective shunt impedance, P the total rf power dissipation in the linac and L the total length of the linac. With A T and r being given a compromise must be found between P and L, since large L makes the beam dynamics more difficult and raises construction cost, and large P makes cooling of the rf structure difficult and raises the operation costs. A reasonable compromise in our case is to dissipate about 20 k W / m ; inserting q5=20 ° and r = 4 0 Mf2/m (see below) we get the desired 9 MeV by dissipating 200 kW of rf power within about 11 m of rf structure. Thus, as compared with pulsed RTMs or RTMs using a superconducting accelerator, the room temperature c.w. R T M has to operate at a relatively high frequency with v = 1, low accelerating field and relatively large spacing between magnets. These choices lead immediately to a major difficulty of this kind of machine: injection problems which are important for other R T M s are even more severe in our case mainly for three reasons: l) Small wavelength and low gradient in the rf structure and large spacing of the magnets call for high injection energy to enable coherent acceleration. 2) Large spacing of the magnets implies relatively weak focusing, resulting in a large beam diameter especially at low energies. 3) A large ratio of magnet spacing to bending radius makes the compensation of the fringe field defocusing rather critical, especially with respect to
chromatic errors and third order aberrations in beam optics (see appendix). To overcome these difficulties relatively high injection energy must be chosen which, however, is rather expensive to achieve in c.w. operation in a conventional manner. Generally, it is seen that injection energy may be lower for the smaller size of the RTM. This suggests the use of a small R T M as an economic injector of a larger one. Point 3 together with the demands for reasonable magnet size and a reasonably low number of recycling loops limit the ratio of output to input energy of a single R T M stage to about 10. (For a pulsed or superconducting R T M the same rule applies if the first linactraversal is considered to be part of the injection,) At electron energies of about 2 MeV or less, phase slip due to low particle velocity becomes so dominant that a R T M does not offer a practical solution any more. Therefore, preacceleration to 2-3 MeV has to be provided by means of a c.w. linac or a dc accelerator. Hence there are three R T M stages necessary to bridge the range from 2 to 820 MeV. Thereby the energy gain ratio of each stage is still less than 10 and this in principle offers the opportunity to accomplish transverse focusing by a quadrupole triplet on the linac axis. (Theoretically, with respect to beam diameter, the decrease of focusing strength with increasing energy is compensated by pseudo-damping.) As compared with focusing by individual quadrupoles on the return paths this method would be very economical and it avoids the otherwise strong coupling between longitudinal and horizontal particle oscillations. Furthermore it offers the advantage of defining the linac axis automatically as the optical axis for all revolutions. This could lead to considerable simplification in adjustment, monitoring and operation of the system. This latter advantage applies also in comparison with split pole focusing which would, moreover, lead to a more complicated magnet construction. A closer look at this kind of focusing shows, however, that it leads to very stringent requirements with respect to field homogeneity in the bending magnets, at least in stages 2 and 3. For these stages we therefore based our design on the less convenient use of quadrupoles on the individual return paths. In stage 1, however, focusing on the linac axis is possible, whereas focusing on the return paths would lead to a severe reduction in acceptance especially in this stage (see below). It should be emphasized that the particular difficulties of our design are at least partly compensated by certain simplifying features: As compared with pulsed RTMs, there are no transient phenomena to care about in our case. Especially we do not have the problem of transient
C. W. R A C E T R A C K
beam loading, and the problem of stability of rf sources may easily be solved by simple control loops, leading to very simple klystron power supplies. Further, at a given average current, c.w. service gives the lowest possible beam emittance which, in turn, helps to meet the more stringent requirements of our machine in this respect. A special advantage of cascading is the fact that the experience gained in constructing and operating a small stage may be used for the construction of the next bigger one, thus reducing the risk for the entire machine considerably. Further we consider it an essential advantage that the two first stages which are relatively inexpensive could provide a c.w. beam of about 100MeV, suitable for a variety of interesting coincidence experiments of the types (e, e'n) and (e,e'7). This by itself could justify the construction of the first two stages. An earlier design of the machine has been given in ref. 9.
3. Optimisation of design parameters and beam optics of M A M I The design is based on the use of the T H O M S O N CSF type T H 2075 c.w. klystron* which gives 50 kW rf power at an efficiency close to 60%. Within its frequency range of (2450_+25)MHz we chose for some practical reasons 2 = 12.240 cm (f=2449.3 MHz). The distance between return paths then becomes 3.896 cm. For optimisation of stages 1 and 2 essentially the following demands had to be taken into account: a) In order to get a 100 MeV beam in a first construction step at the least possible rf expense stages 1 and 2 should be driven by one common klystron. b) Injection energy of stage I should be as low as possible, but high enough to allow coherent acceleration in a straighforward manner. c) The number of turns in stage 1 should be kept sufficiently low so that beam optics are not too much affected by space charge effects. d) Care must be taken that beam optics are not too much affected by higher order aberrations of the fringe field optics of the bending magnets whose influence is approximately proportional to L / R 2 ( L = m a g n e t spacing, R = b e n d i n g radius, see appendix). To evaluate the beam dynamics data of all stages two entirely different computational methods have been used in parallel: 1) An
interactive program called " M E L L Y
* A special version of TH 2054.
7"
MICROTRON
3
running on the medium size computer (CDC 1700) of our laboratory. This program calculates particle trajectories in a similar manner as the program " T R A N S P O R T " lo) does. However, a special matrix algorithm is used which offers the possibility to carry out calculations up to any order; thereby, only non-vanishing matrix elements are stored. In our case, third order proved to be sufficient to take into account all couplings of any significance between different phase space coordinates, a sine-shaped travelling wave in the accelerator and the spherical aberration in the vertical optics of the reverse field lenses of the bending magnets in an analytical approximation (see appendix). This program is very fast and, in connection with some special computer periphery, it is possible to vary several parameters currently by means of potentiometer inputs observing the resultant trajectories on a C R T screen, much as with an analog computer. This p r o g r a m was extremely useful for quick optimisation of parameters. 2) A program called " M I T R A C E " which consists essentially of the " R A Y T R A C E " - p r o g r a m of Enge and Kowalski supplied by a code for tracing particles through an accelerator section. In this program beam optics in the bending magnets were computed using the fringe field shape as measured in a model magnet. Its shape was not optimised for small spheric aberration which gives some margin of safety in this respect. This program has been used to evaluate the phase space transformations through the R T M s by computing many particle trajectories and to investigate the influence of some small errors in field homogeneity on beam optics. It should be mentioned that the fringe field optics of the model magnet have been measured experimentally by deflecting a 200 keV electron beam of well defined, small emittance by 180 °. The condition for infinite vertical focal length and the magnitude of the spherical aberration have been determined and were found to be in good agreement with the M I T R A C E results. In the following we will present the results of numerous computations which lead in a sense to a close to optimum design of beam guidance. It should be kept in mind, however, that so far only two types of focusing systems have been investigated: one using a focusing lens on the linac axis only and the other using alternate singuletts on the return paths only, with constant focal length for all turns. In both cases fringe field optics were adjusted to nearly infinite focal
4
H. H E R M I N G H A U S et al.
TABLE 1
Parameters of MAMI. Stage
1
General Input energy (MeV) Output energy (MeV) Number of turns Distance between magnets (m) (eft. field boundary)
2.11 14.0 21
Magnet Field strength (T) system Radius of inner orbit (m) Radius of outer orbit (m) Gap width (cm) Pole face diameter (m) Magnet diameter (m) Weight (t) (one magnet) Rf system
Beam optics
Number of klystrons Accelerating field amplitude (MeV/m) Electrical length of accelerator (m) Dissipated power (kW) Beam power (kW) (100/IA) Energy gain of synchronous particle (MeV) Synchronous phase angle (deg) Focusing method
Focal length
Normalized input beam emittance ]ongit. (keV.deg) horiz. (moc m m .mrad) vert. (mocm m . m r a d ) Normalized output beam emittance longit. (keV.deg) horiz. (moc m m . r a d ) vert. (moc m m . r a d )
2
14.0 100 43
3
100 820 80
1.66
5.21
0.100 0.086 0.484 2 1.14 1.3 1.2
0.342 1.537 0.142 0.218 0.980 1.781 3 3 2.14 3.72 2.5 5.4 8.5 240 1
0.893 0.71 13.9 1.2 0.588 22
single focusing lens on linac
16 m at l0 MeV
11.83
6
0.512 4.06 26.3 8.6 2.00 16
0.936 10 216 72 9.00 16
quadrupole singlets on the return paths, alternately focusing and defocusing orbit circumference times -k/2
18 n 4.7n 4.5n
26 n 6.7n 6.9n
67n 16n 14n
18 n 4.7n 4.5n
39 n ll.3n 7.0n
105n 34n 16n
length23). In principle, of course, any combination of these methods could be tried and some of them might give better results. The major task of our investigation was, however, to show just o n e possibility that would give satisfactory results. The parameters thus obtained are compiled in table 1, a scaled scheme of the accelerator is shown in fig. 2.
The small gap width in stage 1 is chosen in order to get an accordingly small fringe field length, resulting in low longitudinal dispersion which helps to decrease the input energy. This argument is not crucial for the two other stages. So the gaps may be chosen larger there which helps to keep the more stringent tolerances with respect to field homogeneity. The parameters of the rf systems are calculated assuming an effective shunt impedance of about 40 MQ/m. This is rather low and leaves us some margins to fight multipactoring and cooling problems (see below). The large synchronous phase angle of 22 ° in stage 1 is especially useful in getting low minimum injection energy. A still larger value, however, would lead to a reduced stable phase area in longitudinal phase spaceal'lz), Moreover, we found by numerical calculation using the M E L L Y 7 code that even the 22 ° would lead to instability in stage 1 if transversal focusing were done by alternate singlets in the return paths. This instability appears as if the Q-value of the transverse oscillations were heavily reduced with increasing energy (though quadrupole field strength was chosen proportional to particle momentum), ending up in an integer resonance. The effect is the stronger the smaller the magnet distance and the larger the synchronous phase angle. The effect is amplitude dependent (reduction of bucket size) and it accordingly disappears if only first order transfer matrices are used for computation of the particle trajectories. This instability is also the reason that the synchronous phase angle in stages 2 and 3 is chosen relatively small since in these stages singlets in the return paths have to be used for focusing, for reasons discussed earlier. extraction
.....
~
. . . .
O.X.
guiding magnet 0
'
'
'
'
5rn
--e--
beam
monitor
Fig. 2. Scaled scheme of MAMI. The bumps in the last return paths of stages 1 and 2 serve for longitudinal beam matching.
C. W . R A C E
TRACK
The single focusing lens on the linac of stage 1 may consist of a pair of solenoid lenses, excited oppositely to each other to minimize beam rotation. The quadrupole singlets of stages 2 and 3 may be realized by means of thin copper coils with an outer iron shield. A transversal beam emittance of about 4.5 nmoc m m . r a d and a longitudinal one of 1 8 n d e g ' k e V has been assumed at the entrance of stage 1. This is ample for a beam intensity of 100/tA. In the first stage there is T-2110-(n-05).
588
[ keY ]
21
/.. 100 3
0 C - - : - b2
"50
1
-20
-15
-10
-5
10
15
20 koZ [ o]
Fig. 3. Longitudinal emittance areas in the midst o f the linac o f stage 1 for successive turns (n), T is the kinetic energy o f the electrons, 2110 keV is the kinetic energy o f the s y n c h r o n o u s electron entering stage 1 and 588 keV the energy gain for a relativistic electron passing t h r o u g h the linac at 22 ° (ko = co~c).
MICROTRON
5
practically no spread in phase space since the focusing method used prevents strong coupling between different phase space planes. Entering stage 2, however, some spread has been assumed as a margin for field inhomogeneity, misalignments and matching errors. During acceleration in stage 2 phase space areas are increased, mainly in longitudinal and horizontal phase space, due to coupling by the quadrupole singlets in the return paths. Entering stage 3 a further increase is assumed to allow for field errors, etc. The shapes of the different phase space areas at different locations in the accelerator are shown in figs. 3-6. These areas fill relatively small parts of the acceptance bucket. Their shape is, therefore, mostly rather closely elliptic. Taking into account some further margins of safety it is seen that the beam will leave stage 3 with a transversal emittance of about 3 x x 10 - z n m m ' m r a d at 820 MeV, total energy width being about Ap/p=2x 10 - 4 . AS has been estimated synchrotron radiation effects should not change these data significantly. It should be stressed that these design parameters are chosen to have some margins of safety in beam optics and that we considered it important the whole beam optics to be as straightforward and conservative as possible to ease operation of the machine. For these reasons, for instance, we refrained from using extra
x ' [ mrad ]
"\
/
/
AT [ k e Y ]
stage 2
-05
/
50
in I / / /
\
'\
-04
\
• 0.3
\ \
,. . . . .
.02
'\
'0.1L-"- ~ - . .
1
AT [ keY ]
x[cm]
stage 3
~
OU
'\
x
\
out'3
/
'\
'\ AI.[ o]
]
x-
\
//stage '\
/ \,
/
_/"
1..... 2 ..... 3 - -
_i
Fig. 4. Longitudinal emittance envelopes in the midst o f the linac o f stages 2 and 3 taking into account transversal emittance as shown in figs. 5 and 6.
Fig. 5. H o r i z o n t a l emittance envelopes in the midst o f the linac o f the three stages taking into account vertical and longitudinal emittances as s h o w n in figs. 3, 4 a n d 6 (in: first turn; out: last turn ref. to stages 1 and 3, last but one ref. to stage 2).
6
H. HERMINGHAUS et al.
orbits in the first stage for lower input energy and rather chose a somewhat less economic preaccelerator.
4. Preaccelerator The preaccelerator has to render a beam of 2.11 MeV, containing 100 pA in bunches of 2.4 ° in length and 33.0 keV energy width. As a first alternative we investigated a dc gun of several 100 keV followed by a few short rf accelerator sections with constant phase velocity each. We finally adopted the design shown in fig. 7 which would need about 25 kW of rf power13). The tilt of the phase space volume is correct to match the input admittance of stage l, taking into account the longitudinal dispersion of the injection path. It seems, however, that a Van de Graaff accelerator, equipped with a low power double drift buncher in the terminal would be much more convenient as a preaccelerator, especially with respect to the much less complicated beam dynamics involved. On the other hand it would be markedly more expensive.
intensity, bunch phase and transverse position of the beam with respect to the linac axis at each individual passage and it must be sufficiently sensitive to operate at a beam intensity of 100 pA and less. These requirements may be satisfied using rf resonance cavities as monitors and " m a r k i n g " the beam with short intensity bursts or blackouts. Successive passages may then be identified by the time at which the burst (or blackout) signal appears in the display. For initial optimisation for a run we plan to use a sequence of beam pulses of 12 ns duration - j u s t sufficient to resolve individual passages even in the first stage - at a repetition frequency of about 10 kHz. Thus, during the most critical phase of beam optimisation, the average beam power is too low to cause any harm
chopper, cov. / d.c.gun
1
To take advantage of the feature of individually guided beam loops an adequate monitoring and steering system is inevitable. This system, which will be described in the following, is shown schematically in fig. 8. The monitoring system must be able to determine
I 4BOkeV ~ 1 ~
1/'"
/'//" ,/
/
~--2AOm
beornchopped to 20degrees bunchlength
0.4 . . . . .
/CX ,kov
10¸
~*'2~z
-10"
L03
\
[02
in2 , "\~
out 1.._:_"0~"
in3 ,'
!
/
i
Fig. 7. T h e rf preaccelerator. (a) Scheme of preacceterator; ,Sw = normalized phase velocity. (b) Longitudinal o u t p u t emittance for i n p u t phase range o f 4-12 ° a n d i n p u t energy spread o f 4-1 keV; ko = o)/c.
/
!
/'
Jt
/
I
,/" /
[ "]
~--,.\
J
\,
2.11MeV
0,525m~ ,~T[keV]
l y'[ mrad ] 0,5
in
fl~ 0.978 _/
5. Monitoring and steering
/-
P,,v=Q.g26
./
stoge 1 - - - - . . . . . .
vett~~ hor....-~---J~
Ii n e ~ 7 ~
" rat.
3 Fig. 6. Vertical emittance envelopes in the midst o f the linac o f the three stages taking into account horizontal a n d longitudinal emittances as s h o w n in the figs. 3, 4 a n d 5 (in: first t u r n ; out: last t u r n ref. to stages 1 a n d 3; last but one ref. to stage 2).
int. phase
vert,
hoe
Fig. 8. Monitoring and steering system; D B M : double balanced mixer.
C.W. R A C E T R A C K
to components in case of misalignment. Then beam intensity between the pulses will be increased little by little, successively reoptimizing the operation parameters (essentially rf power and -phase). Finally, at beam intensities of more than half the maximum value, beam blackouts instead of bursts will be used of equal duration and repetition rate. If the dc component is suppressed in the display both burst and blackout mode give identical signals, except for the polarity. The voltage amplitude U o induced by a bunched beam traversing a properly tuned cavity is given by
d~-,'
z
~ J(t);
U
Uo e
,
where r = 2 Q/co is the attenuation time of the field in the cavity, Q its loaded Q-value and F=(VoT)2/W, where Vo is the voltage at the beam position, T the transit-time factor and W the stored energy in the cavity. J(t) is the dc component of the bunched beam intensity. Thus, there are essentially two possible modes of operating a cavity as a fast beam monitor: If r is large compared to the beam pulse duration rB, the above equation gives
it is not difficult to manufacture with sufficient accuracy to get excellent decoupling of the two degenerate modes. Further experiments using a pulsed 200 keV bunched beam of ll ns pulse length showed that the high Q mode operation works very well with the differentiating arrangement as shown in fig. 9. The low Q mode has not yet been tried. Of course, when operating such monitors in an accelerator, care must be taken to keep the high power rf from the cavities and to avoid disturbance from other noise sources. We are qu[te confident, however, to achieve this by inserting cutoff pipes of about l0 cm in length between monitor and linac and by mounting the DBM and a fast video preamplifier immediately at the cavity. Transverse steering will be done in the individual recycling paths as shown in fig. 8. The essential constraint in the construction of the steering elements is given by the small spacing between return paths of
or, after rf detection by a double balanced mixer (DBM) as a phase sensitive device, a s s u m i n g - 7 dB conversion loss and a 50 g2 video load, Uv being the video signal voltage:
tsv~/(5~F)fJdt
(high Q mode).
(4)
b
a
<
ver, lpos.
Iq
Isign.lpr °b_
/ ~[~
Uo F ~ J dt, U° ~ VAT-2
7
MICROTRON
/
',
17
i
II
x.
hot. pos. signalprobe
~f. ~ C H r ef. . . .
I
;added ( ' ~ 1 k.L,/
bH
,nve edJ
CRT I
/ / fe~d through termination M_M2 m cable 50 S2 Fig. 9. (a) rf b e a m position m o n i t o r with experimental setup for high Q m o d e operation. (b) Field pattern as induced by vertical (left) a n d horizontal (right) b e a m offset respectively.
If r is chosen small compared to rB, then Uv ~ ~/(5 Fz)
J
(low Q mode).
(5)
Both operation modes may give about the same video signal amplitude, namely about 5 mV at J = 100/~A, if a single pillbox cavity is used as an intensity and phase monitor. As a beam position monitor a cavity of square cross section may be used which is resonant in the TM210 mode in two directions rectangular to each other (see fig. 9). With such a cavity a video signal of the order of 0.2 mV/mm at 100 ~A is to be expected which is well above detector and preamplifier noise. If desired, the signal-to-noise ratio could be improved considerably by using a sampling technique and raising the prf to 100 kHz. Experiments with a model cavity showed that
k38.96 -~ I ~ I ~
.-~ (
~
.~ beam pipe
horizontal steering colts
.11 .41 ..4 I ~
J~d4
L
~-~\vertical
~ ~
/
"
~
'steering
.
bea.m .p©e t:/eam pipe omitted +horizontal steering coils omitted
coils
Fig. 10. Transverse b e a m steerer, consisting o f an array o f w i n d o w frame m a g n e t s (schematic view a n d cross section, all m e a s u r e s in m m ) .
8
H. H E R M I N G H A U S
3.9 cm only and the necessity o f negligible cross coupling between neighbouring elements. We could meet these requirements by a construction as shown in fig. 10. Measurements with a prototype of 16 cm in length on a 200 keV electron beam showed cross coupling from an excited cell to its next neighbour to be as low as 2 x 10 -3. F r o m there on the stray field decreases further from cell to cell by a factor of about 4 each. This prototype gave a deflecting field of 57 G at 5 A in the coils for horizontal deflection (which are the more critical ones). Thus, a steerer of about 50 cm in length is sufficient to do steering up to 4-1 mrad at 820 MeV. 6. Field errors
We do not see an equally simple method for longitudinal steering, i.e. rf phase correction on successive passages. Field errors o f _+3 x 10 -4 in SBds which will cause 4- 1 mrad deviation in horizontal beam direction m a y cause in the last orbits o f stage 3 a longitudinal shift of 0.7 cm, corresponding to about 20 ° in rf phase. This would be clearly too much if it would change stochastically from turn to turn. It is to be expected, however, that the changes between successive turns will be rather small. In this case one should rather speak of an adiabatic shift in resonant rf phase which would then a m o u n t to about 10 °. This should still be lowered by at least a factor 5 and the best way to do this is to make small field corrections in the region indicated in fig. 11. Experiments with a small model magnet showed that it is possible to make these corrections by locating small pieces of magnetic material in the Purcell-filter between pole piece and yoke. Referring again to transversal beam optics, calculations show that it would not be greatly affected by a smooth field gradient of 10 -4 cm 1. Some care should be taken, however, with respect to the second derivative o f the field and it can be estimated that, in order not to affect markedly the beam proFerties, the gap width
Fig. 11. Most effective region for longitudinal orbit correction.
et al.
should not change by more than 1 Ftm over a distance of typically 1.5 cm (it may change, however, by a larger a m o u n t over distances much shorter or larger than 1.5 cm). In stage 3 these tolerances would be even narrower by about an order o f magnitude if in this stage focusing were done by a single lens on the linac axis only. Referring to unwanted dc or ac magnetic fields, such as the earth's field or fields produced by currents in cables or ground loops, it is easily estimated that their influence on the beam is not dangerous and will be negligible if a thin magnetic shield is applied on the beam guides between the magnets and reasonable care is taken with respect to power cables and grounding. It is seen from the above discussion that much trouble can be avoided if the magnets can be operated always at essentially the same field strength in order to reproduce a field pattern, once optimized, within narrow limits from run to run. 7. Variable energy extraction
Mainly for the reason just mentioned we will change output energy essentially not by varying magnetic field strength (and rf field strength accordingly) but by extracting the beam from one of the inner orbits. The extraction scheme is shown in fig. 12. The return paths pipes within the energy variation range end up downstream in a c o m m o n vacuum c h a m b e r which protrudes by 2 m from the bending magnet. Just in front o f this chamber a special deflection steerer is put over the pipe from which the beam is to be extracted. It is excited to deflect the beam by 35 mrad inwards. The beam then leaves the accelerator in the way shown in fig. 12.
extraction chamber
/
..--------q\ / '[
['movable Jextraction ~-] magnet
\Lo28Testamlox. /35mrad
Fig. 12. Extraction scheme for variable output energy.
9
C.W. R A C E T R A C K M 1 C R O T R O N
The extraction steerer will be made of two easily separable halves and may quickly be clamped over another pipe if a change in output energy is desired. To interpolate between the discrete energies of successive orbits field strengths in deflecting magnets and rf section may be changed by small amounts: changes of -± 1.5% are sufficient to get any energy value down to 300 MeV. 8. Rf structures
Cooling capability and multipactoring are the two main restrictions by which an otherwise good accelerator structure could turn out to be unsuitable for c.w. operation at room temperature. At present we are considering three possible candidates: a) the iris-structure in the SLAC-design14), b) the side coupled structure in the L A M P F designlS.16), c) the jungle gym structure in the design as used at Cornel117.18). The iris structure in the S L A C design can be cooled very effectively because of its rather thick irises: a temperature drop across the iris of no more than about 10°C is to be expected at a power consumption of 20 kW/m. If the structure is designed as a constant gradient structure with small group velocity and an external feedback is used, an overall shunt impedance of about 50 Mf2/m is to be expected at our frequency. In this case, however, the sensitivity of the structure to thermal deformation is very high, so that the temperature at the circumference of the structure finally has to be held constant within a few tenths of a degree and tuning of the section would have to be done under design power operation. Fig. 13 and table 2 show as r ~.10 3
o
/
b
[cml 9.52
IIIIIIIIlllll
\ /
t 18.6kw
3.4 db
12.6 kW
c
950 9.48 120
2b 2a
/ ~40.8 ~'0
10 20 30 40 50 60 z[cm]
radius = 2.8 mm
Fig. 13. Design of the linac o f stage 1 using the iris structure. (a) Parameter variation along the axis, (b) resonant loop, (c) cross section, measures in m m ; cooling is done by 60 axial cooling pipes, formed by grooves 4 mm by 4 m m and an outer water jacket.
TABLE 2 Properties of the linac shown in fig. 13.
Total energy gain Dissipated power Electrical length Mode Beam load derivative Phase change along cold section Phase change along section due to temperature distribution under beam load conditions
0.634 cos 22 ° = 0.588 MeV 11.7 kW 61.2 cm (15 cavities)
2n/3 3.8 MI2 50 °
an example the design of the accelerator section of stage 1. It has been reported that multipactoring at the field levels of c.w. operation can be overcome if some technological precautions are observed19). The side coupled structure offers the highest shunt impedance among all competitors: 65 Mf2/m, if the EPA-structure is scaled to our frequency. Most of this virtue, however, is caused by its narrow aperture of 1.25 cm which might result in beam handling difficulties. But even if the shunt impedance has partly to be sacrificed in favor of a larger aperture there would still remain the advantage of simplicity in operation, without a feedback loop. Presumably temperature differences within this structure would be too high at our power levels unless cooling ducts were provided in the walls between cavities and near the nose cones2°). Little seems to be known about its behaviour with respect to multipactoring in the relevant range of 30 60 keV per cavity. The jungle gym structure has excellent cooling capability, its mechanical tolerances are not critical, it is easy to manufacture and - due to its odd geometry serious difficulties with multipactoring are most unlikely to occurl8). It needs, however, a recirculating loop with high circulating power and its shunt impedance is rather low - the value of 40-Mf2/m given in table I applies for this structure. Thus, for our application the jungle gym structure seems to be the safest, but least economic, choice. At present we are doing some model measurements on this structure. Table 3 gives a rough summary of the properties of the three structures under consideration. Beam break-up (BBU) has not yet been observed in microtrons, to the best of our knowledge. There is, however, an estimation formula by Wilson 21) and a closer investigation by Volodin22). The latter has shown that the Fresence of transverse focusing generally raises the starting current by a large factor. An estimation following ref. 22 shows that even in the
10
H. H E R M I N G H A U S et al.
TABLE 3 General comparison of the three kinds of linac structures under consideration. Structure
Iris (SLAC)
Side-coupled (EPA)
Jungle gym (Cornell)
Mode Group velocity Cooling Tolerances Power handling capability
2n/3 travelling wave 0.0060-0.0037 c good close medium
n/2 travelling wave 0.22 c good wide good
Shunt impedance Pumping Feeding Risk of multipactoring
good medium resonant loop medium
n standing wave 0.04 e difficult medium presumably good, with sophisticated cooling system excellent medium simple unknown
limit of vanishing transverse focusing there is no danger of beam break-up in stage 1. In stages 2 and 3, however, a shunt impedance for the break-up mode of just a few M ~ / m could be sufficient in this case to excite the instability (the estimation formula of ref. 20 gives a somewhat more optimistic result). On the other hand, in stages 2 and 3 there is rather strong focusing by the quadrupoles in the return paths, giving a Q of about 1/8 (Q is about 1/4 with respect to the magnetic period of 2 turns). This should suppress BBU by at least one order of magnitude. Since there are several possibilities left to lower the shunt impedance for the BBU mode of the section substantially we are quite confident that BBU could be overcome in all stages of M A M I .
9. Summary Our design of a room temperature c.w. electron accelerator of 820 MeV output energy leads to a cascade of three S-band race track microtrons with input energies of 2.11, 14 and 100 MeV respectively, fed by a small linac or a Van de Graaff as preaccelerator. In these considerations in general the spherical aberrations of the fringe field optics play a quite significant role. An analytical estimate for these aberrations is generally given in the appendix. Numerous computations of particle trajectories by the aid of two independent computer codes suggest to accomplish focusing at the first R T M by two oppositely excited solenoids on the linac, on the two other RTMs by alternating quadrupole singlets on the return paths. With reasonable margins of safety a beam of 100/~A within an emittance of 3× 1 0 - 2 n m m . m r a d and a relative energy spread of 2 × 10 -4 may be expected at 820 MeV. For lower energy the beam is extracted from one of the inner return paths by the aid of a small inward deflec-
poor excellent resonant loop of high gain low
tion. Monitoring will be done by three rf cavities on the linac axis of each RTM, short intensity bursts or blackouts of the beam serving for orbit identification. Model measurements have been done on some crucial components as bending magnets, beam monitors and special steering elements. Referring to rf structure, cooling capability and multipactoring at our relatively low field gradients are believed to be the main restrictions in our case. There are at present three candidates under consideration: iris structure, side coupled structure and jungle gym structure. A final decision between these requires measurements on short experimental sections under vacuum at full power. Some design studies have been done so far on the iris structure. In the near future special emphasis will be laid on these questions. At present a 50 kW c.w. rf source is being built and some measurements are done on the jungle gym structure. We would like to express our thanks to Prof. A. O. Hanson, Univ. of Illinois, for many informative discussions and his valuable suggestions on the major part of this paper. We would like to thank further the colleagues of our tab and of neighbouring institutes for leaving much operation time on their computers to us.
Appendix: Some
remarks on the reverse field optics
In the following expressions are briefly derived which allow to estimate the spherical aberrations in vertical direction, the dispersion and the coupling of vertical position to longitudinal position occurring during the passage of a beam through a Babic-Sedlacek fringe field23). Using the designations of fig. 14, the Lorentz force
C.W. RACE TRACK MICROTRON in vertical direction reads
Assuming that y remains essentially constant during the passage of the fringe field zone, eq. (6) m a y be written by the aid of eqs. (7) and (8) as
Fy = - evB z sin 0~, which gives
Y' = ~1 {Ylfl B=-Bdz-dlt(B'~zdzlokBo/o --
y,, _ -eB= sin mocfly COS2 (~'
2y3 f : ( B " ~ 2 d z + . . . } , 3 \Bo/
where the dashes mean derivation with respect to z. Using
-el
since--
Bydz,
---
m o c fly
and assuming c~ to be small enough that, for an estimation, cos2~ ~- 1, we get
=
Bz
By dz.
(6)
~ ( y , z ) = - y B + y 3 B " - y 5 -B(4) - + .... 120
(7)
1
_
m
~', 0y
.
B= = -- --c3~e.
c3=
~
L
(B/Bo) 2 dz -
(8)
m.__
-
(B/Bo)
dz ,
(10)
(,,,y --
ft
dz
3 R 2 ,Jo \ B o /
(11)
'
where y is the distance of the b e a m from the middle plane. This corresponds to a spherical aberration. It is seen from eq. (11) that in order to keep this aberration small B' should be distributed rather uniformly over the fringe zone. So the (fictitious) fringe field distributions shown in fig. 15, while all satisfying f0-1 = 0 , should be rather close to the o p t i m u m for small spherical aberrations. A m o n g the curves shown, 1 and 3 give aber-
B(z) pole face
R2
;o
and, if B(z) is chosen in such a way that)Co becomes infinite, the focal length f l for a b e a m off-axis is still finite and given by
,
where B = B ( z ) is the field in the middle plane ( y = 0 ) . Then
(9)
where z = 0 ... l denotes the fringe field zone, B o is the field inside the magnet and R the radius of curvature of the particle trajectory there. F r o m this it is seen that the focal length f o for particles near the middle plane is given by
fo Generally, a plain static field, symmetrical with respect to the (x, z)-plane, m a y be derived from a potential
By -
11
1 b =B,~'I/~.(~- ~1)
Bo
ac rive clamp y/x b z
...a-¢ Fig. 14. Definition of symbols and coordinates used in the appendix,
Fig. 15. Examples for close to optimum field distributions giving infinite vertical focal length.
12
H. HERMINGHAUS et al. o f the b e a m as a f u n c t i o n o f its vertical d i s p l a c e m e n t y in the fringe z o n e is c a l c u l a t e d a p p r o x i m a t e l y to be
r a t i o n s o f equal strength, lower t h a n 2, given by
Ax = y2/2R,
This is j u s t 3 times the error p r o d u c e d by a n ideally straight fringe field o f the s a m e l e n g t h w i t h o u t c o m p e n s a t i o n o f vertical defocusing. The field d i s t r i b u t i o n o f a m o d e l m a g n e t w h i c h was n o t o p t i m i s e d with respect to low a b e r r a t i o n s a n d was t h u s r a t h e r far f r o m the n e a r o p t i m u m d i s t r i b u t i o n s o f fig. 15 (I) gives, f o l l o w i n g M I T R A C E , a 1.32 times larger value. This d i s t r i b u t i o n has b e e n used t h r o u g h o u t the M 1 T R A C E c o m p u t a t i o n s . T h e l o n g i t u d i n a l disp e r s i o n s o f d i s t r i b u t i o n s 1 a n d 3 are o b t a i n e d by s t r a i g h t f o r w a r d rectification o f the trajectories. F o r a w h o l e 180 ° b e n d i n g m a g n e t the t r a j e c t o r y l e n g t h S is in case 1 : S = rrR + 21 [0.788675 + 0.002726 ( l / R ) 2 ] , in case 3 : S = ~R + 21 [ - 0.28868 + 0.07089 ( l / R ) 2 ] . (13) So b o t h d i s t r i b u t i o n s give a c o n t r i b u t i o n to longit u d i n a l d i s p e r s i o n o f the s a m e sign as a particle with e n e r g y d e p e n d e n t velocity does, b u t in case 1 this c o n t r i b u t i o n is m u c h smaller. So case 1 is to be preferred t h o u g h case 3 m a y have the a d v a n t a g e n o t to need a n active field c l a m p a n d to result in a s m a l l e r pole face area. C o m p a r i n g eqs. (12) a n d (13) it is seen t h a t m a k i n g the fringe field d e p t h l large m a y result in small spherical a b e r r a t i o n s in vertical b e a m optics, b u t l o n g i t u d i n a l l y the a d d i t i o n a l phase shift w h i c h is i n t r o d u c e d b y a n y fringe field at low b e n d i n g radii is increased a n d vice versa. By i n t e g r a t i n g -e x " -- - By(z, y), m o cfl~
u s i n g eqs. (7) a n d (8), the h o r i z o n t a l d i s p l a c e m e n t A x
(14)
which is i n d e p e n d e n t o f the f o r m o f the fringe field. This is i d e n t i c a l with the e x p r e s s i o n used in the " T R A N S P O R T " - p r o g r a m 1°) for n o r m a l fringe fields.
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