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Electron injectors for linear accelerators
NUCLEAR INSTRUMENTS AND
METHODS
IO 5
(I972) 335-347;
©
NORTH-HOLLAND
PUBLISHING
CO.
ELECTRON INJECTORS FOR LINEAR ACCELERATORS D. T R O N C
Ddpartement Accdldrateurs, TI-[OMSON-CSF, B.P. no. 10, 91 Orsay, France Received 27 December 1971 and in revised form 3 July 1972 The effects of the input electron energy, of the modulation and drift space choice for a prebunching device, of the field and length choice for a first " l o n g " cell and of the accelerating " s y n c h r o n o u s " structure itself are computed leading to the evaluation of the gun voltage effect on the bunching performances,
to a simple model describing the prebunching with space-charge effect and to the improvement in p e r f o r m a n c e s - together with very low sensitivity to parameters variations around the design values - obtained with a first asynchronous cell. Electron injector designs are presented.
1. Introduction
The accelerating process in an electron linear accelerator requires the injection of the particles in discrete bunches phased on the travelling-wave and at an energy of a few MeV. The injector is the device taking the dc or pulsed electron beam out of the electron gun and packing it in the tight bunches which must have a low axial extension and a low energy ,dispersion.
introduction of a new device, a first long cell in the iris loaded structure, can improve the bunching quality and allow acceleration of higher beam currents. This system is quite simple and makes prebunching and chopping less critical. The T H O M S O N - C S F injectors use a long cell in the rf power coupler. Large variations of parameters around the design values are allowed. Their effects are described by simple relations.
It is generally an iris loaded transmission wave guide designed specially to perform the accelerating/ bunching process. It can be preceded by a prebuncher :modulator cavity and a drift space1'2). In some cases a chopper is added to remove the unwanted electrons. The present paper deals with the computation methods for the design of injectors and the selection of critical parameters. The computation tools which allow 1:he study of the dynamic interaction of an electron beam with the acceleration electric field are described, with or without a magnetic focusing field. If required the repulsion forces between the relativistic electrons (space charge effects) can also be included. These computation tools are then used in a discus,;ion of the two main parameters in the injector design: the gun voltage and the average electric field in the iris loaded structure. The study based on a dc beam and neglecting space charge effects shows that the parameters are not critical in a proper design. A moderate gun voltage only is required. The prebunching process, including space charge effects, is then analyzed for moderate gun voltages. The quantitative results obtained lead to a simple model and an expression is derived which can be useful for the selection of design parameters for a given beam current. In these investigations it was discovered that the
With all these elements it is possible to show how the injector components can be fitted together. The step by step design process which has been found the most successful is described as we think it can be more useful to designers than to quote only results. It can be used for the simple injectors of sturdy medical or industrial accelerators of for the high resolution injector of a physics research machine, where prebunching and chopping are used. Some definitions will be helpful. In what follows we call "synchronous" iris structure an iris structure in which the position of the center of the accelerated bunch of electrons relative to the crest of the accelerating field has a slow variation when measured between middle planes of successive cavities. We call " n a t u r a l " bunching the corresponding dynamic process in such a structure. The "phase law" represents the slow variation of dephasing between electrons and crest of the field measured between middle planes of successive cavities. It is remembered that electrons cross a succession of resonant cavities so that the precise law of dephasing has a saw-tooth appearance around the (mean) "phase law" as defined. Our computations take account of the precise law. The "phase law" depends of the choice of the lengths of the cavities as measured along the acceleration axis. If a cavity has a great length we call it a "long cell". Such a "long cell" can be useful and leads to large and different
335
336
D. T R O N C
phase-shifts for electrons in the bunching process, for moderate energy3'4). 2. Electron beam and accelerating structure simulation Calculations were done on a U N I V A C 1106/8 with our ESPEL computer program 1) which simulates a relativistic electron beam submitted to an axial oscillating electrical field. Amplitudes and phases of this field along the beam axis can be given in one of the following ways: a) as a preset analytical law, b) as points along the axis if measurements done on a model are available. In this case which corresponds to the calculations done for designs analyzed below, these measurements of field amplitude and phase take care of the z dependance inside the first cells (which could also be included in the analytical treatment as harmonics). The bell shape of the field inside the long cavity which includes a part of the input coupler in T H O M S O N - C S F design has been measured in travelling wave s) as well as in standing wave6), c) as a preset field amplitude law together with a computed phase law which gives a preset phase trajectory to one electron defined by its input phase and energy. Then the preset field amplitude must be somewhat corrected afterwards as different phase laws correspond to different lengths of the cells in a practical design. Space charge effect can be included as the beam is simulated by a certain number of separate discs of equal and homogeneous density of particles. Usually radial effects are not included in the computations and a constant radius is given to the beam which means that a proper axial magnetic field is applied. The error arising from this restriction is low if this field is several times the Brillouin value. However, the radius a of each disc can be computed from the value of the radial electric field
Q
rO d__m_m+ m (rO + 2 Of) = - elBa. dt The longitudinal dynamics is there computed with the interaction field added to the preexistant rf field. For a disc (i): E~(i) = ERF COS(Pi
q- ~
Q F 2ij
2iJ
2
2 -- - 2.½/
i=~ 2rcajeo [_lzlj[
(aj +zi~) d
~
where (Pi is its average phase for one step, Q is the disc charge and aj the radius of disc j, zli is the distance with relativistic correction between discs ( i ) a n d (j) (fig. 1). The approximations are as follows: 1) Interaction fields due to space charge are supposed constant along each step; this approximation leads to a cumulative error which can become sizeable in a slow bunching or debunching process especially in prebunching calculations. 2) The beam is simulated by a cylinder of finite length. One wavelength of the rf field is necessary for a prebunching calculation and this excludes analytical models for prebunching based on a cylinder of short phase extension. 3) The number of discs is limited and can be very low: this observation leads to a simplified model concept presented below leading to a compression formula for prebunching. 4) The expression of the interaction field corresponds only to the field applied to the center of disc (i). 5) The distances between discs are calculated from their phase positions at the end of a step (time of arrival at z corresponding to the step) with the help of velocities corresponding to different times. A more precise computation would be based on the mean value between their velocities at one time and their velocities at one position on the axis. However this error on space-charge interaction decreases with the distance between discs.
Er - 2~ze°a d , Er
of a long beam cylinder in which the density is a function of the distance d between the two neighbouring discs, and from the value of the axial magnetic field Bz. In this case, the equations of dynamics in cylindrical coordinates are integrated: i" dm + m ( f _ r 0 2 ) = e(Er + rOBz) ' dt
Z
[
IzlJl
I I ~
i-I
II1
211" R F f i e l d
I ' )
l a~,so, I . . . . '°"°°
Bz ,Ez ( R F field)
Fig. 1. Electron beam simulation.
ELECTRON
INJECTORS
FOR LINEAR
337
ACCELERATORS
90
e# •
•
•
..:
1 •
/ .°o
•
. . g Y.
•
. . . . • °°
0
•
/
/
I
0
•
! L
910
45
I A.^OVi 135
Fig. 2a. O u t p u t p h a s e extension vs i n p u t p h a s e extension for 40 ~< 1/"o~< 400 keV a n d 2.5 ~< E~< 20 M V / m . T h e origins o f phases are different for different values o f (l/0, E).
3. "Natural" bunching The influence of the input electron energy on the performances of a synchronous iris structure (" natural" buncher) must be considered first as the selection of the gun dc accelerating voltage is an important decision leading to quite different designs and costs. The experience on accelerators already built shows that similar results can be expected with either a low energy injection of 40 keV 4'7) or a higher injection of
i
> O=loo
2o-
~.~,._.__.~.--
n
AW 10 °/o
W "
10-
¥
I ----I
Z
~"-=2.~
~ I
AW-7% --~-
-
~.0:,° _ . ¢ ~ . I aw=ls°/o
iz 2.5-
I11 ,,J I11 L! g
°"~-~ 4b
,I 120 400 ' ' INJECTION [KEV]
Fig. 2b. Lines of constant output extension of phases for 90° a~Lthe input (dashed lines) and 45 ° at the input (solid lines) and lines of constant dispersion of energies for 90° at the input (dots and dash lines) as function of injection and accelerating field.
120 k e y 7) or even 400 keV8). This is confirmed by the results presented below. These results show also that the amplitude of the accelerating field is not critical and not linked in first approximation with the input electron energy as was sometimes reported. Calculation of the final bunching process in a synchronous iris structure for different values of the accelerating field and of the energy of electrons at the input has been done so that one injected electron remains at the same phase trajectory and determines a computed phase law as indicated before. We choose - 4 5 ° for this synchronous phase (the maximum field occurs for zero phase) which corresponds to a strong compression together with adequate acceleration. The field is assumed constant along the structure to simplify the comparisons. Its variation is in fact moderate and can further be controlled with realistic slow changes of iris diameters for a travelling wave structure. Computations for 3 values of the injection energy (40, 120, 400 keV) and 4 values of the accelerating field E (2.5, 5, 10, 20 MV/m) lead to comparable final phase extensions at 6.6 MeV. The shapes of the curves giving the output phase versus the input phase are similar for the 12 cases even if the best bunching occurs around different input and output phases. In fig. 2a the curves are shifted for superposition. The calculated positions of electrons are given alone (dots) for clarity together with an average parabolic fitting curve. The bunching quality does not depend much on the values
338
D. TRONC
of the parameters for a selected phase or the bunch along a synchronous structure. Fig. 2b gives the quantitative results. The curves (drawn by interpolation between computed results) represent constant final phase extensions of 20 to 35 °, for 90 ° input (dashed lines) and of 6 to 10°, for 45 ° input (solid lines). The final energy dispersion varies between 6 to 10% (dot and dash lines) for 90 ° input. For example, an injection energy of 40 keV and an accelerating field of 6 MV/m give an output bunch extension of 6 to 8 ° for 45 ° at the input or 20 to 25 ° for 90 ° at the input and the energy dispersion in this last case is around 7% at 6.6 MeV. For each computation done we select the 45 ° or 90 ° input phase extensions giving the lowest output phase extension. Usually it corresponds also to the lowest energy dispersion and lies n e a r the - 4 5 ° synchronous
phase. The "natural" buncher has a total input phase acceptance of 140° to 180 ° on 360 ° . For a good compression of the central part of the bunch, Elies between the usual values of 3 to 12 MV/m. There is no limitation on the injection energy. However, the extremities of the bunch are further apart for very high injection energy (see dashed lines for 90 ° at the input) as the "rigidity" of electrons is increasing. The energy dispersion decreases with E. The best results giving a compression ratio better than 7.5 for 45 ° input but decreasing strongly with the input phase extension correspond to a low energy and a strong field (40 keV, l0 MV/m). Space charge effects and improvements in these performances of a "natural" buncher by the choice of a first long cavity will be discussed below (sections 5 and 7).
4. Choice of the prebunching parameters
2
ENERGY
[KEV]
Fig. 3a
9 n" 1
1" O.
0
30
50 ENERGY(KEV)
Fig. 3b Fig. 3. Phase vs energy for drift spaces of 4.5 cm (a), 6 cm (b), 7.5 cm (c), 12 cm (d). (3 GHz, injection at 40 keV, modulation ± 12 kV, beam diameter 5 mm, current of 2A.) Density distributions are shown at the right for drift spaces of 4.5 and 7.5 cm.
Electrons are slowed down during the first half of an rf cycle and accelerated during the second half of the same cycle when they cross a modulation cavity. The following drift space transforms the velocity modulation into a phase bunching. Computations are made with space-charge and relativistic effects. Fig. 3 illustrates the results for one example, giving the plot of phase versus energy computed for different drift lengths for an injection of 40 keV electrons, a 3 G H z frequency modulation with + 12 kV amplitude, a beam diameter of 5 ram, and a 2 A current for which the high space-charge does not allow the discs to cross each other. Three charts give useful quantitative results for designs for injection at 40 keV, 3 GHz frequency and a constant beam diameter of 5 mm: 1) The compression (defined as the ratio of the phase extension for the best possible choice of the drift space to an initial selected phase extension) versus intensity, for different modulation amplitudes. Continuous and dashed lines correspond respectively to 150 ° and 90 ° initial phase extensions in fig. 4a. 2) The energy dispersion in the bunch versus intensity in the same conditions (fig. 4b). 3) The drift space values corresponding to the highest compression values for 120° initial phase extension, versus intensity (fig. 4c). Tabulated results (table 1) including effects of an axial magnetic field give a good agreement with constant beam diameter results for strong focusing and show that the necessary magnetic field must increase
ELECTRON INJECTORS FOR LINEAR ACCELERATORS strongly with the current a n d will be the limiting factor for very high currents. The c o m p u t e d n o r m a l i z e d m a i n radius increase for the central electrons o f the b u n c h inside a 90 ° initial phase extension is given t o g e t h e r with magnetic field a n d compression, m o d u l a t i o n , current, drift space. These c o m p u t a t i o n s lead to the following c h r o n o logical i n t e r p r e t a t i o n for the p r e b u n c h i n g process in the case o f high current: 1) The p h a s e b u n c h i n g c o r r e s p o n d s to a m a x i m u m a p p e a r i n g in the p r e v i o u s l y u n i f o r m charge density d i s t r i b u t i o n in the beam. This creates u n c o m p e n s a t e d space-charge forces accelerating the first low energy discs (discs slowed d o w n b y the m o d u l a t i o n cavity d u r i n g the first h a l f o f the rf Z 0
cycle) and decelerating the last discs of high energy. There is energy equalization as well as phase bunching (fig. 3, curves a a n d b; a n d fig. 4b
with decreasing energy dispersion when current increases). This shows that for strong space-charge effects a strong modulation and a short drift space do
not necessarily lead to an inconvenient high energy dispersion at the entrance o f the following accelerating structure. 2) Debunching begins early at the center of the bunch where discs repel each other strongly a n d relative velocities are inverted. Inside a wave-front starting f r o m the center a n d e x p a n d i n g t o w a r d s
the extremities exists a domain with a uniform density decreasing with time as electrons separate f r o m each other. A t the same time the electrons
o~
20
f~ tU IT
339
belonging to the outside domains are still in the b u n c h i n g process a n d are accelerated o r slowed
down as a whole (fig. 3 curves b and c).
0 U 5 3 2 i 0.5
i 1
l 2
I 3
I 5
I 10
INTENSITY
( A )
Fig. 4a. Maximum compressions are given for an initial phase extension of 90 ° (dashed lines) and 150° (solid lines). The analytical formulation given in the text leads to the dash-dot curves.
The wave-front c o r r e s p o n d s to two m a x i m a o f density as inner a n d outer discs have o p p o s i t e relative velocities a n d get very close before equalizing their energies. 3) The two regions outside the central d o m a i n o f decreasing density are progressively d i s a p p e a r i n g a n d d e b u n c h i n g occurs with general equalization o f energies. H o w e v e r some discs o f the central d o m a i n can " j u m p " outside being strongly accel-
15-
0.5>. 0 . 3 ~9 IZ 0 . 2 Ill
[d] ~oooooooooooeoooOOee rC 1
U
"Xo \
z
IIJ u, 0 . 1 Q
• • •
~e~eeeeeeLoJ°°*eeee e e
°ooe
°°~..
UJ tl d IZ
~
10-
Z 00.0501 rr
[]
tU O, 01
[cl
ooooooo o o o o o o o o o o o o o o o ~
5
[d] I
0.5
I
I
I
I
/
1
2
3
5
10
INTENSITY
( A )
n
0.5
i
I
~
2
u
3
~
5 INTENSITY
Fig. 4b. Relative dispersions of energy around the mean energy of 40 keV corresponding to maximum compression (see fig. 4a) are given for an initial phase extension of 120 °.
110 (A)
Fig. 4c. Drift space values corresponding to maximum compression (see fig. 4a) are given for an initial phase extension of 120°.
Fig. 4. Prebunching with space-charge effect for a frequency of 3 GHz, a beam diameter of 5 mm, injection at 40 keV, four values of modulations: 4-5 kV (a), 4-8 kV (b), ± 12 kV (c), 4-18 kV (d).
340
D. T R O N C TABLE 1 Results of c o m p u t a t i o n including radial effect for a n initial b e a m diameter o f 5 m m , injection at 40 keV, 3 G H z .
Modulation (kV)
Current (A)
Drift space for maximum compression (cm)
-4-5 5:5 4-8 4- 12 4- 12 4- 12
0.6 0.6 1.5 3.0 3.0 6.0
14.5 14.5 9.0 6.0 6.0 6.0
crated or decelerated by the high densities of the central domain and afterwards by the even higher densities of the wave-fronts. They are included into "islands" of very high and very low energies (fig. 3, curve d) during the debunching period. We have here an example of the principle of acceleration (or deceleration) by space-charge effects alone. However, this is not realistic as the computation is done with a model of several tens of discs in one dimension only. The best drift space value (fig. 4c) does not change much with current and the analytical value calculated without space-charge effect can be taken as a basis for design. Its variation can be explained. For moderate currents the inversions of velocities or wave-fronts do not appear or appear late in the process and the numerous discs from the sides determine the compression value. The space-charge effect reduces somewhat the difference of velocity between the two sides as if a lower initial modulation had been applied corresponding to an increase for the best drift space value: the curve has a positive slope for moderate currents. But when the wave-front appears early it determines the best drift space value which must be shortened so that the wave-front has no time to expand too much: the curve has a negative slope for high currents. The compression value (fig. 4a) can be computed analytically with the help of a simple model. It is known that the expression of the axial electrical field created by an homogeneous beam cylinder does not change if the cyclinder is replaced by two discs coincident with its bases9). In the greater part of the bunching process the initial one-wavelength beam which is a cylinder of 2~ radians does not remain homogeneous
Magnetic focussing field (T)
0.07 0.05 0.10 0.20 0.15 0.15
A v e r a g e Maximum radius compression increase
1.13 1.29 1.19 1.13 1.34 1.24
5.3 5.8 6.0 7.3 7.6 4.2
but its density has a rather smooth variation (before debunching or expansion of the wave-front). A model with four discs at distances of k~Z from each other (this distance leading to a correct simulation of the modulation) and symmetrical with respect to the center of the 2~ cylinder is chosen as an approximation. Fig. 5 giving the phase energy plot computed with many discs without and with space-charge and positions computed with the same space-charge for four discs shows the agreement in results especially about phase positions.
~'ob
L I.
1-
°1',1' ,21 I
I °
('
_o___ Ja
\',
I
I
}I
/
/
', / ~ob c
t 10 KEV 10 KHV t
J
Fig. 5. Comparison of multi-discs computations (a and b) and of 4 discs model (c). (a) and (c) correspond to 4A, (b) to 0A.
ELECTRON
INJECTORS
FOR
Taking account of the symmetry of the model the dynamics of only two discs have been investigated in the system of reference moving with the bunch, neglecting relativistic effects: ½m[~2(1) - ~o2(1)-1 = 2e
(E2~1 +E3--,, +Ezl.--,1) dx,
½mE~,~(2) - ~o~(2)2 = 2e io (E,-~2+E3-.2+F~4-.2)dx. ~o (i) is the initial speed of the disc (i), ~t (i) the speed at the time when the best compression occurs, Ei-~j the axial field of the disc (i) on the disc (j). For computation of the distances between discs when bunching occurs we need the speeds of the discs. A simple and at the same time realistic assumption is to cancel the relative speed of the two central discs without modification of the speeds of the external discs. The further hypothesis that distances between central and external discs does not change leads to the the use of only one equation. ~2(2 ) _
2e__.QQI--f(L) +f(lO + f ( / x + L ) - f ( 2 L ) ] ,
rmraeo with f ( x ) = I x l - (1 +x2) ~. Q is the charge of one disc, a its radius, l 1 the distance between the central discs for the bunching, L the initial distances between the discs, normalized respective to the radius (fig. 5). #2(2 ) _
2e [Vo(2) ½ _
~o~]2.
m
Vo (2) is the initial energy of a central disc, V0 is the initial average energy and the equation becomes:
LINEAR
341
ACCELERATORS
and l given by
f(1) -- f ( 2 L ) - 0.0555 aF° U2
Ire Compressions for three values of the modulation are plotted in fig. 4a (lines with dots and dashes) and lie well between results of computations previously done with many discs for initial phase extensions of 90 ° and 150 °. (Then L = 3.74, f ( l ) = - 0 . 0 7 - 0 . 0 1 0 4 U2/L If for example U = 12 kV, I = 3A, then f(1) = - 0 . 5 5 , 1 = 0.64, giving a compression ratio of 5.8). 5. Introduction of a first "long cavity"
Investigations in the bunching given by an accelerating structure with phase law synchronous with the center of the electron bunch show the possibility of injecting electrons bunched in phase even if there is a high energy dispersion. For a half-meter long synchronous structure with an electrical field of 5 MV/m bunch phase extensions of the same order are obtained with electrons injected with a phase extension of 90 ° around - 4 5 ° at the same energy of 60 keV or from electrons injected at the same phase of - 4 5 ° and energies between 40 and 80 keV. Usually electrons crossing each other early in a synchronous accelerating structure cannot be avoided as the phase of the bunch in the process of formation must be kept well behind the crest of the field. This "convergence" is enhanced by use of a prebunching results and leads to the choice of a low prebunching modulation together with a long drift space and the corresponding sensitivity to space-charge effects. The use of a first long cavity has the prebunching effect of a modulation cavity followed by a drift space
[1/o(2) + - Vo~]2 = f(ll) +f(ll +L) - f ( L ) - - f ( 2 L ) A V Ckey)
(x
"~ f(ll) - f(2 L), with ~ = 1.11 x 10 - l ° a/Q, a in ram, Q in C, Vin keV. The disc charge Q is one-fourth the ratio of the current on the rf frequency (with a negative sign), L = ¼2off~a, and Vo(2) = Vo___U/x/2 (notations given below). For IVo(2) - Vol'~ Vo, the equation leads to the following simple expression giving an evaluation of the compression L/l with strong space-charge effect for given values of radii a (ram), rf frequency Fe (GHz), current I(A), peak to peak modulation amplitude U(kV), initial beam energy Vo(keV) and speed fl = v/c: L = 75fl
aFo
0,2-
-40
0.1-
-20
/
. . . . . . '_r"~ (~j,vO
~ a
~ ~
---,-z
~o;,~,+..
" ' V° = V; + Z~V
(%,Vo) 10
25
I 30
ZPt r" m] 4 0
Fig. 6. Output phase and energy for the central electron around which bunching occurs for different lengths of a long cavity (input 40 keV, field 4 MV/m).
342
D. T R O N C TArtLY 2 C o m p r e s s i o n , energy dispersion and quality index for injectors o f fig. 7.
Injector
Aq~i (rad)
Aq~0 (rad)
Compression
Quality index
A~v~/A~o
A Vo
k
Vo A+B B" A+B B'
1.4 0.8 0.8 0.8
0.1 0.1 0.04 0.l
14 8 20 8
together with a possibility of control of the convergence; the cavity itself combines modulation and drift space and its length is much shorter; this can be of great advantage when space-charge problems occurs with high currents. As this cavity can be the first cell of the structure there is no need for an independent rf power input nor for a critical phase control. Relativistic calculations done step by step for a long cavity with constant field show that the initial phase of the electrons which lie at the center of the bunching at the cavity output is near - n (the maximum field occurs for zero phase) and depends little on the field strength and the cavity length. For a central electron initially at an energy of 40 keV and for a field of 4 MV/m, the output phase is (Po = ¢p~+~h for the input "central" phase q~i = - 2 . 8 rad. c~ is slowly decreasing as the length h increases. The output energy Vo = V~+A V reaches a maximum of 40 keV for h = 26 m m and decreases afterwards. Fig. 6 gives the variation of ~ and A V with the length of a long cell assuming a constant field. A good bunching at the cavity output occurs at a phase of about + ½n for the electrons near the maximum value of the output energy for the central electron. Computation of the dynamics of such an injector
~o
0.038 0.038 0.021 0.042
1.75 1.0 5.0 1.0
with a first long cell ( A + B ) and of an equivalent injector (B') has been done. Fig. 7 and table 2 represent the two injectors with their field and phase law together with values of compression, energy dispersion, "quality index" values. Improvement by a factor of two is obtained on the phase compression for a given initial phase extension or on the phase admittance at the input for a given compression. A buncher including a first long cell is equivalent to a classical synchronous buncher with a well optimized prebunching system. Advantage results from simplicity of design and flora the absence of critical prebunching parameters modified by space-charge effects. If a prebunching is added to such a buncher, acceptance in phase can be increased even more with a lower sensitivity to prebunching parameters and linked space-charge effects. 6. Influence of parameter adjustments on characteristics of a buncher with a first long cell
For the Saclay Linac (A.L.S.) design l°) which has a first long cell (however not optimized) a systematic review of the influence of the variations of parameters around the design values was done and the following results were obtained: ACCELERATED
CURRENT
rI'
100%
L.
5O°/°
-'7
z
~
o
E=4MeV/m
mm E=5MeV/m
13_ _1_..13 Iq L = 50Omm
fl
I 20
L 30
I 40
I 50
l 60
INPUT
E N E R G Y (keV1
E-- 5MeV/m
Fig. 7. Injectors with and without a first long cell.
Fig. 8. Accelerated current without p r e b u n c h i n g for three values o f rf power (or accelerating field) a n d variable injection energy.
343
ELECTRON I N J E C T O R S FOR L I N E A R A C C E L E R A T O R S
1) The phase acceptance which corresponds to the accelerated current without prebunching decreases with the injection energy Vi and the level of the accelerating field E. The variation is proportional to the simple product ViE or Vi,~/P. Fig. 8 illustrates this variation: r/ = 3 . 0 ( V ~ x / P - 25),
laws of dependance can be explained at least qualitatively as the phase compression occurs mostly at the beginning of the buncher where the bunch phase is not synchronous with the axial field but see it at all possible phases. This leads to a bunch of quite uniform density in function
Vi < 50keV.
c_ o UJ
r/ is the ratio of the accelerated current on the total injected current, Vi is given in keV, P is the rf injected power in MW. The design values for this buncher were Vi = 40 keV, P = 1.3 MW. For greater injection values r/can be as high as 80% and progressively returns to the asymptotic value of 50% corresponding to the time during which the field is accelerating. The bunching effect of the first long cell is responsible for q greater than the "theoretical" expected value of 50%. 2) At the output of the buncher the phase extension Aq~o and the energy dispersion AVo/Vo are not sensitive to Vi or E. This corresponds to calculation results for designs discussed below (see fig. 14d and text). 3) A~0o changes linearly with the considered input phase extension Aq~i (fig. 9, curve a) but A Vo/Vo changes as a power of Aq~ (fig. 9, curve b). These
POWER
(
P MW
)
0.75
1
1.5
I
I
I
o
<~ o ~10%E G 01 )-
--15 I/~ < 1" --30 IZ
-15° ~
I--45 -I O. I-
X -10" ~
D
n
,,E, 5%-
z W
-5 ° ~
v
I
I _Q
a
2'5 a,b_
~o
ACCEPTANCE
7'5 (z~01/2rl
en°/o)
Fig. 9. Computed phase extension (curve a) and energy spread (curve b) at the output of ALS buncher for different acceptance values. Output phase of the bunch for different rf power (or accelerating field) values.
E MV/m 5-
3
!
/
4 O
2
I
1
O
I , , I, to I
100 28
160
I
_o, zL
30
500
synchronous
I
900
(ram)
buncher
5 4
b
3
,
I !
'
2 1
O
]
,
,'oo • 4.,
,5
,,
,,
,o
~2
3oo/,oo 24
2,
,
,
,'oo
Z (ram)
,oo
synchronous
buncher
Fig. 10. Accelerating field values along z-axis for travelling wave buncher designs (a) and (b) (discussed in text) and including the use of prebunching. Lengths of the modulation cavity, of the drift space, when prebunching is used, and of the first cells of the structure are given. The dephasing between adjacent cells of the two structures is ~zt.
344
D. T R O N C
of its phase extension. But the energy spread occurs afterwards, when the bunch is synchronous with the accelerating field and near its crest. Then: A V0 __ k ( c o s q g l _ c o s 9 2 )
Vo = 2k sin ~PI +-@2 sin ¢Pl-9/02 2 2
~,
--
½k(Aq~)2,
with qh = 0 (one side of the bunch at the crest) and tp2 = +Acp. 4) The bunching occurs around an output mean phase ~Po which changes with the level of the accelerating field E so that the output mean energy of the bunch is kept constant (fig. 9, curve c). For Saclay design ~/P cos ~oo = de=0.86. This explains why, when for other applications a variable energy accelerator is needed, it is necessary to use a short bunching structure followed by a synchronous structure and to adjust the phase shift between them.
7. Designs of electron injectors A long cavity for which the mean output energy is close to the maximum is used: its length is 26 m m in the conditions of fig. 6. The field's bell shape inside this cavity requires in practice the use of a greater length for comparable results. At the end of such a cavity the bunch is ahead of the crest of the field and it will be necessary to shift the bunch behing the crest, in the phase bunching region. This is done through the help of the phase variation between this first long cell and the following cell together with an asynchronous law of phase chosen for the trajectory of the bunch along the three or four first cells.
For a given mode of operation with a given dephasing between cells this is achieved by proper selection of the lengths of these cells, which are slightly shorter than required for synchronism for the average energy value at the output of the long cell. This corresponds to the synchronism for an energy of 40 keV at the input of the long cell. The 2n/3 mode of operation is selected. Fig. 10 gives the field values along the z-axis together with lengths of cells for the designs discussed below, including the prebunching which can be used if improved results are needed. The entrance of this premodulation cavity is taken as origin. The field values of the first design (a) correspond to a travelling wave structure with coupling irises of 18 m m for 0.7 M W of rf power or 22 m m for 1.4 M W for 3 G H z and iris thickness of 3 ram. The results obtained below will be more easily understood if a lens representation for the bunching process is used. Fig. 11 gives such an optical analogy for several designs. Monoenergetic input electrons correspond to parallel rays, before the first lens. The axis corresponds to the "central" trajectory around which bunching occurs and the two optical rays correspond to two electrons representative of the bunching process. They are chosen well inside the phase acceptance domain at a short distance from the "central" electron. They usually "cross" each other after several cavities. (This optical model is valid only for a limited part of the phase acceptance domain as outer electrons have a different behaviour: they are less compressed and usually do not "cross" each other.) A bunching/accelerating iris structure is represented by two successive convergent lenses (2) and (3) in fig. 11. The lens (2) represents either the bunching
0
b
1
-0.5-
¢
I
I
-4
INPUT
Fig. 11. Lens representation for bunching process in several different designs (see text).
I
I
-2
PHASE
RAD.
Fig. 12. Output phase vs input phase without prebunching and without (curve a) or with (curve b) a 28 m m long cavity. See fig. l l a .
ELECTRON
INJECTORS
FOR LINEAR
effect of the first "synchronous" cells of a natural buncher or the effect of a first " l o n g " cell alone in other designs. The phase domain extension valid for the analogy used is larger with a long cell. Crossing of central electrons occurs inside the bunch and the lens (3) represents the bunching effect of the remaining cells of the structure where electrons are behind the crest of the wave, in the convergent region. Electrons do not cross each other later as the increase of energy "freezes" the bunch. When prebunching is added as in fig. 1 l b and c a convergent lens (1) accounts for the presence of the modulation cavity. For a " n a t u r a l " buncher the overall behaviour depends strongly on the distance between this prebunching cavity and the iris structure. In most cases, its value must be different from the " b e s t " drift space value as defined for prebunching alone. Then the design problem for an injector corresponds to the proper choice of the lenses, positions and convergences. The convergence depends on the phase law followed by the bunch center for a given accelerating field level. 1) Fig. 12 gives the output phase (for z = 860 m m and an energy of 2.9 MeV) versus the input phase (z -- 170 mm) for the field values of fig. 10a, with or without a first long cell. There is no prebunching. The bunching is excessive and the electrons cross each other leading to a negative slope of the two phase diagrams. The crossing occurs around the third cell, early in the accelerating process. A~oo/d~o ~= 0 . 2 5 without the long cell, Aq~o/A~Pl = 0.13 with a long cell. These two cases correspond to fig. 11 a but the lens (2) has a lower convergence when it corresponds to the beginning of the structure including a first long cell, and this explains the better overall compression value. The
345
ACCELERATORS
two phase laws were chosen to give a similar number of accelerated electrons. A further decreasing of the convergence would be obtained at the expense of this number.
2) Fig. 13 gives the output phase (z = 860 mm) versus the input phase (z = 0) for an effective modulation of -t-5 kV and for an optimized drift space value of 160 mm. This value is greater than the best compression value of 120 m m for prebunching alone as the excessive convergence of the accelerating structure must be corrected. This choice corresponds to fig. l l c to be compared to fig. l l b which would give a worse result on the final bunch extension than without prebunching even if the number of accelerated electrons has increased. Without a long cavity (fig. 13, curve a) the bunch has a phase extension of 13 ° (for 230 ° input) with a rather uniform density at the center and two maxima of density at its extremities. With a long cavity the bunching of a// the accelerated electrons is comparable (fig. 13, curve b) but the bunch is very different and one half of the accelerated electrons are very strongly compressed. Furthermore variations of prebunching parameters are much less important. If a chopper is included in the design before the modulation cavity a bunch of a few degrees can be expected (90 ° input inside 1° output). Space-charge effect has been computed as the long drift space together with the very strong bunching for half of the r~ 0 < rr Ill m
< z
e-o.5 I-
Io
-1
-6
-5 J
. . . . . .
-3
-0.5
-4 I
-2 INPUT
I
]
I
I
I
-5
-4
-3
-2
-1
INPUT
PHASE
-0 HAIti.
Fig. 13. O u t p u t p h a s e vs i n p u t p h a s e with p r e b u n c h i n g without (curve a) or with (curve b) a long cavity. See fig. l l a .
-3 [
T -- -- -- r
-2 I
T
-1 PHASE
I l
0 HAD.
Fig. 14. O u t p u t p h a s e vs i n p u t p h a s e without p r e b u n c h i n g for design o f fig. l l b . C o m p a r i s o n o f curves a a n d b shows the i m p r o v e m e n t obtained with a long cavity. Curves c a n d d show that the length o f the long cell or the field level are n o t critical for the b u n c h i n g quality (only the o u t p u t average p h a s e changes). Lower scale o f i n p u t p h a s e corresponds to curve a, upper scale corresponds to curves b, c, d.
346
D. T R O N C
electrons increases its effect. For a beam diameter of 2.5 m m and a gun current of 50 mA, 12 mA (or 90 ° input) are bunched well inside 2 ° . 3) The level of the field decreases to three-quarters of its preceding values and fig. 14 compares the output phases at an energy of 2.5 MeV versus the input phase with and without a first long cell. The long cell has been lengthened by 4 m m and the lengths of the following cells increase more slowly (fig. 10b). The bunching is now optimized. 60% of the output electrons are inside a 4 ° bunch corresponding to an initial extension of 130 ° (fig. 14b). Without the long cell, crossing occurs again (fig. 14a). Sensitivity to variation of parameters has been analyzed for this design: in fig. 14c the long cavity is reduced by 3 mm, in fig. 14d the fields are increased by 22%. This design leads to a very simple injector, useful for example for medical or industrial applications without prebunching and with no provision for adjustment of electrical parameters. There is only a phase adjustment between the bunching structure and the following synchronous structure if a high energy is needed when rf power is increased. Similar results can be obtained with a biperiodic or a triperiodic standing wave structure. 4) A premodutation cavity with its drift space is added to these structures. The drift space is taken equal to 75 m m with the long cavity and 112 m m
d rr tu
0
a" IX
I-
~
-O.E
-1
I -5
I -4
I -3
I -2 INPUT
I -1 PHASE
I -0 gAD.
Fig. 15. O u t p u t p h a s e vs input p h a s e with p r e b u n c h i n g for design o f fig. 1 lb. C o m p a r i s o n of curves a a n d b shows that the drift space choice (or the modulation) is critical without a long cell. C o m p a r i s o n o f curves c a n d d shows that p r e b u n c h i n g parameters are n o t critical with a long cell.
TABLE 3 Space-charge effect for design o f fig. l i b with long cavity a n d prebunching.
Injected current I0 (mA)
Accelerated current In (mA)
0 50 100 200
0 38 75 150
B u n c h extension (°) 0.75 la 2.5 MeV
0.75 Is 4.7 MeV
0.5 Is 4.7 M e V
8.2 6.2 7.0 7.9
4.6 5.3 6.5
2.3 2.8 4.2
without it, for a modulation of + 4 kV. Fig. 15 gives the corresponding output phases at a 2.5 MeV level versus the input phase before the modulation cavity. When prebunching is added to a " n a t u r a l " buncher, results become comparable to performances of a buncher with a long cavity but without prebunching (fig. 15a). However, this system is very sensitive to the drift space length (and to space-charge effects which require a variation of this parameter), to the phase adjustment between premodulation field and the structure field and to the level of premodulation. In particular if the drift space is 75 m m instead of 112 m m (or if the premodulation is decreased) the bunching is destroyed (fig. 15b). With prebunching added to the buncher with a long cavity the number of accelerated electrons is increased. The drift space length (or level of premodulation) is not at all critical as shown in figs. 15c and d, this last figure corresponding to a drift space of 112 mm. The convergence has been increased but the crossing occurs far in the structure and the space-charge has a favourable effect. Space-charge effect was computed for a beam of 2.5 m m diameter between 0 and 200 mA and results are given in table 3. A chopper added to this design will give a bunch of 20 mA and 1° to 2 ° phase extension for a high performance linear accelerator. The advantages on other designs are the lower cost of the gun and its modulator together with low sensitivity to premodulation level and phase misadjustments. References 1) D. Tronc, Electron p r e b u n c h i n g with space-charge effects, 1971 Particle Accelerator C o n f . - I E E E Trans. Nucl. ScL NS-18, no. 3 (1971) 550.
E L E C T R O N I N J E C T O R S FOR L I N E A R A C C E L E R A T O R S z) K. R. Crandall and C. R. Emigh, MP4/KC2, part B (1967). 3) Patent 70 39.261. 4) H. Leboutet and D. Tronc, Improvement of the bunching in injectors for electron linacs, 1971 Particle Accelerator Conf. (1971) p. 558. 5) K. B. Mallory and R. H. Miller, On non-resonant perturbation measurements, IEEE Trans. MTT (1966) 99. 6) B. Epsztein and D. Tronc, Phase measurement along linac sections by a resonant method, 1966 Linac Acc. Conf. (Los Alamos, 1966)p. 198.
347
7) p. Brunet and X. Buffet, Electron injectors, B.2.1., in: Linear accelerators (eds. P. Lapostolle and A. Septier; NorthHolland Publ. Co., Amsterdam, 1970) p. 247. 8) j. Haimson, A low emittance high duty factor injector linac, 1971 Particle Accelerator Conf. (1971) p. 592. 9) E. Durand, Eleetrostatique, vol. I (Masson, Paris) p. 333. 10) G. Azam, A. Bensussan, H. Leboutet and D. Tronc, ALS, caract6ristiques du faisceau d'61ectron, l'Onde Electrique (Dec. 1969) 1136.
METHODS
IO 5
(I972) 335-347;
©
NORTH-HOLLAND
PUBLISHING
CO.
ELECTRON INJECTORS FOR LINEAR ACCELERATORS D. T R O N C
Ddpartement Accdldrateurs, TI-[OMSON-CSF, B.P. no. 10, 91 Orsay, France Received 27 December 1971 and in revised form 3 July 1972 The effects of the input electron energy, of the modulation and drift space choice for a prebunching device, of the field and length choice for a first " l o n g " cell and of the accelerating " s y n c h r o n o u s " structure itself are computed leading to the evaluation of the gun voltage effect on the bunching performances,
to a simple model describing the prebunching with space-charge effect and to the improvement in p e r f o r m a n c e s - together with very low sensitivity to parameters variations around the design values - obtained with a first asynchronous cell. Electron injector designs are presented.
1. Introduction
The accelerating process in an electron linear accelerator requires the injection of the particles in discrete bunches phased on the travelling-wave and at an energy of a few MeV. The injector is the device taking the dc or pulsed electron beam out of the electron gun and packing it in the tight bunches which must have a low axial extension and a low energy ,dispersion.
introduction of a new device, a first long cell in the iris loaded structure, can improve the bunching quality and allow acceleration of higher beam currents. This system is quite simple and makes prebunching and chopping less critical. The T H O M S O N - C S F injectors use a long cell in the rf power coupler. Large variations of parameters around the design values are allowed. Their effects are described by simple relations.
It is generally an iris loaded transmission wave guide designed specially to perform the accelerating/ bunching process. It can be preceded by a prebuncher :modulator cavity and a drift space1'2). In some cases a chopper is added to remove the unwanted electrons. The present paper deals with the computation methods for the design of injectors and the selection of critical parameters. The computation tools which allow 1:he study of the dynamic interaction of an electron beam with the acceleration electric field are described, with or without a magnetic focusing field. If required the repulsion forces between the relativistic electrons (space charge effects) can also be included. These computation tools are then used in a discus,;ion of the two main parameters in the injector design: the gun voltage and the average electric field in the iris loaded structure. The study based on a dc beam and neglecting space charge effects shows that the parameters are not critical in a proper design. A moderate gun voltage only is required. The prebunching process, including space charge effects, is then analyzed for moderate gun voltages. The quantitative results obtained lead to a simple model and an expression is derived which can be useful for the selection of design parameters for a given beam current. In these investigations it was discovered that the
With all these elements it is possible to show how the injector components can be fitted together. The step by step design process which has been found the most successful is described as we think it can be more useful to designers than to quote only results. It can be used for the simple injectors of sturdy medical or industrial accelerators of for the high resolution injector of a physics research machine, where prebunching and chopping are used. Some definitions will be helpful. In what follows we call "synchronous" iris structure an iris structure in which the position of the center of the accelerated bunch of electrons relative to the crest of the accelerating field has a slow variation when measured between middle planes of successive cavities. We call " n a t u r a l " bunching the corresponding dynamic process in such a structure. The "phase law" represents the slow variation of dephasing between electrons and crest of the field measured between middle planes of successive cavities. It is remembered that electrons cross a succession of resonant cavities so that the precise law of dephasing has a saw-tooth appearance around the (mean) "phase law" as defined. Our computations take account of the precise law. The "phase law" depends of the choice of the lengths of the cavities as measured along the acceleration axis. If a cavity has a great length we call it a "long cell". Such a "long cell" can be useful and leads to large and different
335
336
D. T R O N C
phase-shifts for electrons in the bunching process, for moderate energy3'4). 2. Electron beam and accelerating structure simulation Calculations were done on a U N I V A C 1106/8 with our ESPEL computer program 1) which simulates a relativistic electron beam submitted to an axial oscillating electrical field. Amplitudes and phases of this field along the beam axis can be given in one of the following ways: a) as a preset analytical law, b) as points along the axis if measurements done on a model are available. In this case which corresponds to the calculations done for designs analyzed below, these measurements of field amplitude and phase take care of the z dependance inside the first cells (which could also be included in the analytical treatment as harmonics). The bell shape of the field inside the long cavity which includes a part of the input coupler in T H O M S O N - C S F design has been measured in travelling wave s) as well as in standing wave6), c) as a preset field amplitude law together with a computed phase law which gives a preset phase trajectory to one electron defined by its input phase and energy. Then the preset field amplitude must be somewhat corrected afterwards as different phase laws correspond to different lengths of the cells in a practical design. Space charge effect can be included as the beam is simulated by a certain number of separate discs of equal and homogeneous density of particles. Usually radial effects are not included in the computations and a constant radius is given to the beam which means that a proper axial magnetic field is applied. The error arising from this restriction is low if this field is several times the Brillouin value. However, the radius a of each disc can be computed from the value of the radial electric field
Q
rO d__m_m+ m (rO + 2 Of) = - elBa. dt The longitudinal dynamics is there computed with the interaction field added to the preexistant rf field. For a disc (i): E~(i) = ERF COS(Pi
q- ~
Q F 2ij
2iJ
2
2 -- - 2.½/
i=~ 2rcajeo [_lzlj[
(aj +zi~) d
~
where (Pi is its average phase for one step, Q is the disc charge and aj the radius of disc j, zli is the distance with relativistic correction between discs ( i ) a n d (j) (fig. 1). The approximations are as follows: 1) Interaction fields due to space charge are supposed constant along each step; this approximation leads to a cumulative error which can become sizeable in a slow bunching or debunching process especially in prebunching calculations. 2) The beam is simulated by a cylinder of finite length. One wavelength of the rf field is necessary for a prebunching calculation and this excludes analytical models for prebunching based on a cylinder of short phase extension. 3) The number of discs is limited and can be very low: this observation leads to a simplified model concept presented below leading to a compression formula for prebunching. 4) The expression of the interaction field corresponds only to the field applied to the center of disc (i). 5) The distances between discs are calculated from their phase positions at the end of a step (time of arrival at z corresponding to the step) with the help of velocities corresponding to different times. A more precise computation would be based on the mean value between their velocities at one time and their velocities at one position on the axis. However this error on space-charge interaction decreases with the distance between discs.
Er - 2~ze°a d , Er
of a long beam cylinder in which the density is a function of the distance d between the two neighbouring discs, and from the value of the axial magnetic field Bz. In this case, the equations of dynamics in cylindrical coordinates are integrated: i" dm + m ( f _ r 0 2 ) = e(Er + rOBz) ' dt
Z
[
IzlJl
I I ~
i-I
II1
211" R F f i e l d
I ' )
l a~,so, I . . . . '°"°°
Bz ,Ez ( R F field)
Fig. 1. Electron beam simulation.
ELECTRON
INJECTORS
FOR LINEAR
337
ACCELERATORS
90
e# •
•
•
..:
1 •
/ .°o
•
. . g Y.
•
. . . . • °°
0
•
/
/
I
0
•
! L
910
45
I A.^OVi 135
Fig. 2a. O u t p u t p h a s e extension vs i n p u t p h a s e extension for 40 ~< 1/"o~< 400 keV a n d 2.5 ~< E~< 20 M V / m . T h e origins o f phases are different for different values o f (l/0, E).
3. "Natural" bunching The influence of the input electron energy on the performances of a synchronous iris structure (" natural" buncher) must be considered first as the selection of the gun dc accelerating voltage is an important decision leading to quite different designs and costs. The experience on accelerators already built shows that similar results can be expected with either a low energy injection of 40 keV 4'7) or a higher injection of
i
> O=loo
2o-
~.~,._.__.~.--
n
AW 10 °/o
W "
10-
¥
I ----I
Z
~"-=2.~
~ I
AW-7% --~-
-
~.0:,° _ . ¢ ~ . I aw=ls°/o
iz 2.5-
I11 ,,J I11 L! g
°"~-~ 4b
,I 120 400 ' ' INJECTION [KEV]
Fig. 2b. Lines of constant output extension of phases for 90° a~Lthe input (dashed lines) and 45 ° at the input (solid lines) and lines of constant dispersion of energies for 90° at the input (dots and dash lines) as function of injection and accelerating field.
120 k e y 7) or even 400 keV8). This is confirmed by the results presented below. These results show also that the amplitude of the accelerating field is not critical and not linked in first approximation with the input electron energy as was sometimes reported. Calculation of the final bunching process in a synchronous iris structure for different values of the accelerating field and of the energy of electrons at the input has been done so that one injected electron remains at the same phase trajectory and determines a computed phase law as indicated before. We choose - 4 5 ° for this synchronous phase (the maximum field occurs for zero phase) which corresponds to a strong compression together with adequate acceleration. The field is assumed constant along the structure to simplify the comparisons. Its variation is in fact moderate and can further be controlled with realistic slow changes of iris diameters for a travelling wave structure. Computations for 3 values of the injection energy (40, 120, 400 keV) and 4 values of the accelerating field E (2.5, 5, 10, 20 MV/m) lead to comparable final phase extensions at 6.6 MeV. The shapes of the curves giving the output phase versus the input phase are similar for the 12 cases even if the best bunching occurs around different input and output phases. In fig. 2a the curves are shifted for superposition. The calculated positions of electrons are given alone (dots) for clarity together with an average parabolic fitting curve. The bunching quality does not depend much on the values
338
D. TRONC
of the parameters for a selected phase or the bunch along a synchronous structure. Fig. 2b gives the quantitative results. The curves (drawn by interpolation between computed results) represent constant final phase extensions of 20 to 35 °, for 90 ° input (dashed lines) and of 6 to 10°, for 45 ° input (solid lines). The final energy dispersion varies between 6 to 10% (dot and dash lines) for 90 ° input. For example, an injection energy of 40 keV and an accelerating field of 6 MV/m give an output bunch extension of 6 to 8 ° for 45 ° at the input or 20 to 25 ° for 90 ° at the input and the energy dispersion in this last case is around 7% at 6.6 MeV. For each computation done we select the 45 ° or 90 ° input phase extensions giving the lowest output phase extension. Usually it corresponds also to the lowest energy dispersion and lies n e a r the - 4 5 ° synchronous
phase. The "natural" buncher has a total input phase acceptance of 140° to 180 ° on 360 ° . For a good compression of the central part of the bunch, Elies between the usual values of 3 to 12 MV/m. There is no limitation on the injection energy. However, the extremities of the bunch are further apart for very high injection energy (see dashed lines for 90 ° at the input) as the "rigidity" of electrons is increasing. The energy dispersion decreases with E. The best results giving a compression ratio better than 7.5 for 45 ° input but decreasing strongly with the input phase extension correspond to a low energy and a strong field (40 keV, l0 MV/m). Space charge effects and improvements in these performances of a "natural" buncher by the choice of a first long cavity will be discussed below (sections 5 and 7).
4. Choice of the prebunching parameters
2
ENERGY
[KEV]
Fig. 3a
9 n" 1
1" O.
0
30
50 ENERGY(KEV)
Fig. 3b Fig. 3. Phase vs energy for drift spaces of 4.5 cm (a), 6 cm (b), 7.5 cm (c), 12 cm (d). (3 GHz, injection at 40 keV, modulation ± 12 kV, beam diameter 5 mm, current of 2A.) Density distributions are shown at the right for drift spaces of 4.5 and 7.5 cm.
Electrons are slowed down during the first half of an rf cycle and accelerated during the second half of the same cycle when they cross a modulation cavity. The following drift space transforms the velocity modulation into a phase bunching. Computations are made with space-charge and relativistic effects. Fig. 3 illustrates the results for one example, giving the plot of phase versus energy computed for different drift lengths for an injection of 40 keV electrons, a 3 G H z frequency modulation with + 12 kV amplitude, a beam diameter of 5 ram, and a 2 A current for which the high space-charge does not allow the discs to cross each other. Three charts give useful quantitative results for designs for injection at 40 keV, 3 GHz frequency and a constant beam diameter of 5 mm: 1) The compression (defined as the ratio of the phase extension for the best possible choice of the drift space to an initial selected phase extension) versus intensity, for different modulation amplitudes. Continuous and dashed lines correspond respectively to 150 ° and 90 ° initial phase extensions in fig. 4a. 2) The energy dispersion in the bunch versus intensity in the same conditions (fig. 4b). 3) The drift space values corresponding to the highest compression values for 120° initial phase extension, versus intensity (fig. 4c). Tabulated results (table 1) including effects of an axial magnetic field give a good agreement with constant beam diameter results for strong focusing and show that the necessary magnetic field must increase
ELECTRON INJECTORS FOR LINEAR ACCELERATORS strongly with the current a n d will be the limiting factor for very high currents. The c o m p u t e d n o r m a l i z e d m a i n radius increase for the central electrons o f the b u n c h inside a 90 ° initial phase extension is given t o g e t h e r with magnetic field a n d compression, m o d u l a t i o n , current, drift space. These c o m p u t a t i o n s lead to the following c h r o n o logical i n t e r p r e t a t i o n for the p r e b u n c h i n g process in the case o f high current: 1) The p h a s e b u n c h i n g c o r r e s p o n d s to a m a x i m u m a p p e a r i n g in the p r e v i o u s l y u n i f o r m charge density d i s t r i b u t i o n in the beam. This creates u n c o m p e n s a t e d space-charge forces accelerating the first low energy discs (discs slowed d o w n b y the m o d u l a t i o n cavity d u r i n g the first h a l f o f the rf Z 0
cycle) and decelerating the last discs of high energy. There is energy equalization as well as phase bunching (fig. 3, curves a a n d b; a n d fig. 4b
with decreasing energy dispersion when current increases). This shows that for strong space-charge effects a strong modulation and a short drift space do
not necessarily lead to an inconvenient high energy dispersion at the entrance o f the following accelerating structure. 2) Debunching begins early at the center of the bunch where discs repel each other strongly a n d relative velocities are inverted. Inside a wave-front starting f r o m the center a n d e x p a n d i n g t o w a r d s
the extremities exists a domain with a uniform density decreasing with time as electrons separate f r o m each other. A t the same time the electrons
o~
20
f~ tU IT
339
belonging to the outside domains are still in the b u n c h i n g process a n d are accelerated o r slowed
down as a whole (fig. 3 curves b and c).
0 U 5 3 2 i 0.5
i 1
l 2
I 3
I 5
I 10
INTENSITY
( A )
Fig. 4a. Maximum compressions are given for an initial phase extension of 90 ° (dashed lines) and 150° (solid lines). The analytical formulation given in the text leads to the dash-dot curves.
The wave-front c o r r e s p o n d s to two m a x i m a o f density as inner a n d outer discs have o p p o s i t e relative velocities a n d get very close before equalizing their energies. 3) The two regions outside the central d o m a i n o f decreasing density are progressively d i s a p p e a r i n g a n d d e b u n c h i n g occurs with general equalization o f energies. H o w e v e r some discs o f the central d o m a i n can " j u m p " outside being strongly accel-
15-
0.5>. 0 . 3 ~9 IZ 0 . 2 Ill
[d] ~oooooooooooeoooOOee rC 1
U
"Xo \
z
IIJ u, 0 . 1 Q
• • •
~e~eeeeeeLoJ°°*eeee e e
°ooe
°°~..
UJ tl d IZ
~
10-
Z 00.0501 rr
[]
tU O, 01
[cl
ooooooo o o o o o o o o o o o o o o o ~
5
[d] I
0.5
I
I
I
I
/
1
2
3
5
10
INTENSITY
( A )
n
0.5
i
I
~
2
u
3
~
5 INTENSITY
Fig. 4b. Relative dispersions of energy around the mean energy of 40 keV corresponding to maximum compression (see fig. 4a) are given for an initial phase extension of 120 °.
110 (A)
Fig. 4c. Drift space values corresponding to maximum compression (see fig. 4a) are given for an initial phase extension of 120°.
Fig. 4. Prebunching with space-charge effect for a frequency of 3 GHz, a beam diameter of 5 mm, injection at 40 keV, four values of modulations: 4-5 kV (a), 4-8 kV (b), ± 12 kV (c), 4-18 kV (d).
340
D. T R O N C TABLE 1 Results of c o m p u t a t i o n including radial effect for a n initial b e a m diameter o f 5 m m , injection at 40 keV, 3 G H z .
Modulation (kV)
Current (A)
Drift space for maximum compression (cm)
-4-5 5:5 4-8 4- 12 4- 12 4- 12
0.6 0.6 1.5 3.0 3.0 6.0
14.5 14.5 9.0 6.0 6.0 6.0
crated or decelerated by the high densities of the central domain and afterwards by the even higher densities of the wave-fronts. They are included into "islands" of very high and very low energies (fig. 3, curve d) during the debunching period. We have here an example of the principle of acceleration (or deceleration) by space-charge effects alone. However, this is not realistic as the computation is done with a model of several tens of discs in one dimension only. The best drift space value (fig. 4c) does not change much with current and the analytical value calculated without space-charge effect can be taken as a basis for design. Its variation can be explained. For moderate currents the inversions of velocities or wave-fronts do not appear or appear late in the process and the numerous discs from the sides determine the compression value. The space-charge effect reduces somewhat the difference of velocity between the two sides as if a lower initial modulation had been applied corresponding to an increase for the best drift space value: the curve has a positive slope for moderate currents. But when the wave-front appears early it determines the best drift space value which must be shortened so that the wave-front has no time to expand too much: the curve has a negative slope for high currents. The compression value (fig. 4a) can be computed analytically with the help of a simple model. It is known that the expression of the axial electrical field created by an homogeneous beam cylinder does not change if the cyclinder is replaced by two discs coincident with its bases9). In the greater part of the bunching process the initial one-wavelength beam which is a cylinder of 2~ radians does not remain homogeneous
Magnetic focussing field (T)
0.07 0.05 0.10 0.20 0.15 0.15
A v e r a g e Maximum radius compression increase
1.13 1.29 1.19 1.13 1.34 1.24
5.3 5.8 6.0 7.3 7.6 4.2
but its density has a rather smooth variation (before debunching or expansion of the wave-front). A model with four discs at distances of k~Z from each other (this distance leading to a correct simulation of the modulation) and symmetrical with respect to the center of the 2~ cylinder is chosen as an approximation. Fig. 5 giving the phase energy plot computed with many discs without and with space-charge and positions computed with the same space-charge for four discs shows the agreement in results especially about phase positions.
~'ob
L I.
1-
°1',1' ,21 I
I °
('
_o___ Ja
\',
I
I
}I
/
/
', / ~ob c
t 10 KEV 10 KHV t
J
Fig. 5. Comparison of multi-discs computations (a and b) and of 4 discs model (c). (a) and (c) correspond to 4A, (b) to 0A.
ELECTRON
INJECTORS
FOR
Taking account of the symmetry of the model the dynamics of only two discs have been investigated in the system of reference moving with the bunch, neglecting relativistic effects: ½m[~2(1) - ~o2(1)-1 = 2e
(E2~1 +E3--,, +Ezl.--,1) dx,
½mE~,~(2) - ~o~(2)2 = 2e io (E,-~2+E3-.2+F~4-.2)dx. ~o (i) is the initial speed of the disc (i), ~t (i) the speed at the time when the best compression occurs, Ei-~j the axial field of the disc (i) on the disc (j). For computation of the distances between discs when bunching occurs we need the speeds of the discs. A simple and at the same time realistic assumption is to cancel the relative speed of the two central discs without modification of the speeds of the external discs. The further hypothesis that distances between central and external discs does not change leads to the the use of only one equation. ~2(2 ) _
2e__.QQI--f(L) +f(lO + f ( / x + L ) - f ( 2 L ) ] ,
rmraeo with f ( x ) = I x l - (1 +x2) ~. Q is the charge of one disc, a its radius, l 1 the distance between the central discs for the bunching, L the initial distances between the discs, normalized respective to the radius (fig. 5). #2(2 ) _
2e [Vo(2) ½ _
~o~]2.
m
Vo (2) is the initial energy of a central disc, V0 is the initial average energy and the equation becomes:
LINEAR
341
ACCELERATORS
and l given by
f(1) -- f ( 2 L ) - 0.0555 aF° U2
Ire Compressions for three values of the modulation are plotted in fig. 4a (lines with dots and dashes) and lie well between results of computations previously done with many discs for initial phase extensions of 90 ° and 150 °. (Then L = 3.74, f ( l ) = - 0 . 0 7 - 0 . 0 1 0 4 U2/L If for example U = 12 kV, I = 3A, then f(1) = - 0 . 5 5 , 1 = 0.64, giving a compression ratio of 5.8). 5. Introduction of a first "long cavity"
Investigations in the bunching given by an accelerating structure with phase law synchronous with the center of the electron bunch show the possibility of injecting electrons bunched in phase even if there is a high energy dispersion. For a half-meter long synchronous structure with an electrical field of 5 MV/m bunch phase extensions of the same order are obtained with electrons injected with a phase extension of 90 ° around - 4 5 ° at the same energy of 60 keV or from electrons injected at the same phase of - 4 5 ° and energies between 40 and 80 keV. Usually electrons crossing each other early in a synchronous accelerating structure cannot be avoided as the phase of the bunch in the process of formation must be kept well behind the crest of the field. This "convergence" is enhanced by use of a prebunching results and leads to the choice of a low prebunching modulation together with a long drift space and the corresponding sensitivity to space-charge effects. The use of a first long cavity has the prebunching effect of a modulation cavity followed by a drift space
[1/o(2) + - Vo~]2 = f(ll) +f(ll +L) - f ( L ) - - f ( 2 L ) A V Ckey)
(x
"~ f(ll) - f(2 L), with ~ = 1.11 x 10 - l ° a/Q, a in ram, Q in C, Vin keV. The disc charge Q is one-fourth the ratio of the current on the rf frequency (with a negative sign), L = ¼2off~a, and Vo(2) = Vo___U/x/2 (notations given below). For IVo(2) - Vol'~ Vo, the equation leads to the following simple expression giving an evaluation of the compression L/l with strong space-charge effect for given values of radii a (ram), rf frequency Fe (GHz), current I(A), peak to peak modulation amplitude U(kV), initial beam energy Vo(keV) and speed fl = v/c: L = 75fl
aFo
0,2-
-40
0.1-
-20
/
. . . . . . '_r"~ (~j,vO
~ a
~ ~
---,-z
~o;,~,+..
" ' V° = V; + Z~V
(%,Vo) 10
25
I 30
ZPt r" m] 4 0
Fig. 6. Output phase and energy for the central electron around which bunching occurs for different lengths of a long cavity (input 40 keV, field 4 MV/m).
342
D. T R O N C TArtLY 2 C o m p r e s s i o n , energy dispersion and quality index for injectors o f fig. 7.
Injector
Aq~i (rad)
Aq~0 (rad)
Compression
Quality index
A~v~/A~o
A Vo
k
Vo A+B B" A+B B'
1.4 0.8 0.8 0.8
0.1 0.1 0.04 0.l
14 8 20 8
together with a possibility of control of the convergence; the cavity itself combines modulation and drift space and its length is much shorter; this can be of great advantage when space-charge problems occurs with high currents. As this cavity can be the first cell of the structure there is no need for an independent rf power input nor for a critical phase control. Relativistic calculations done step by step for a long cavity with constant field show that the initial phase of the electrons which lie at the center of the bunching at the cavity output is near - n (the maximum field occurs for zero phase) and depends little on the field strength and the cavity length. For a central electron initially at an energy of 40 keV and for a field of 4 MV/m, the output phase is (Po = ¢p~+~h for the input "central" phase q~i = - 2 . 8 rad. c~ is slowly decreasing as the length h increases. The output energy Vo = V~+A V reaches a maximum of 40 keV for h = 26 m m and decreases afterwards. Fig. 6 gives the variation of ~ and A V with the length of a long cell assuming a constant field. A good bunching at the cavity output occurs at a phase of about + ½n for the electrons near the maximum value of the output energy for the central electron. Computation of the dynamics of such an injector
~o
0.038 0.038 0.021 0.042
1.75 1.0 5.0 1.0
with a first long cell ( A + B ) and of an equivalent injector (B') has been done. Fig. 7 and table 2 represent the two injectors with their field and phase law together with values of compression, energy dispersion, "quality index" values. Improvement by a factor of two is obtained on the phase compression for a given initial phase extension or on the phase admittance at the input for a given compression. A buncher including a first long cell is equivalent to a classical synchronous buncher with a well optimized prebunching system. Advantage results from simplicity of design and flora the absence of critical prebunching parameters modified by space-charge effects. If a prebunching is added to such a buncher, acceptance in phase can be increased even more with a lower sensitivity to prebunching parameters and linked space-charge effects. 6. Influence of parameter adjustments on characteristics of a buncher with a first long cell
For the Saclay Linac (A.L.S.) design l°) which has a first long cell (however not optimized) a systematic review of the influence of the variations of parameters around the design values was done and the following results were obtained: ACCELERATED
CURRENT
rI'
100%
L.
5O°/°
-'7
z
~
o
E=4MeV/m
mm E=5MeV/m
13_ _1_..13 Iq L = 50Omm
fl
I 20
L 30
I 40
I 50
l 60
INPUT
E N E R G Y (keV1
E-- 5MeV/m
Fig. 7. Injectors with and without a first long cell.
Fig. 8. Accelerated current without p r e b u n c h i n g for three values o f rf power (or accelerating field) a n d variable injection energy.
343
ELECTRON I N J E C T O R S FOR L I N E A R A C C E L E R A T O R S
1) The phase acceptance which corresponds to the accelerated current without prebunching decreases with the injection energy Vi and the level of the accelerating field E. The variation is proportional to the simple product ViE or Vi,~/P. Fig. 8 illustrates this variation: r/ = 3 . 0 ( V ~ x / P - 25),
laws of dependance can be explained at least qualitatively as the phase compression occurs mostly at the beginning of the buncher where the bunch phase is not synchronous with the axial field but see it at all possible phases. This leads to a bunch of quite uniform density in function
Vi < 50keV.
c_ o UJ
r/ is the ratio of the accelerated current on the total injected current, Vi is given in keV, P is the rf injected power in MW. The design values for this buncher were Vi = 40 keV, P = 1.3 MW. For greater injection values r/can be as high as 80% and progressively returns to the asymptotic value of 50% corresponding to the time during which the field is accelerating. The bunching effect of the first long cell is responsible for q greater than the "theoretical" expected value of 50%. 2) At the output of the buncher the phase extension Aq~o and the energy dispersion AVo/Vo are not sensitive to Vi or E. This corresponds to calculation results for designs discussed below (see fig. 14d and text). 3) A~0o changes linearly with the considered input phase extension Aq~i (fig. 9, curve a) but A Vo/Vo changes as a power of Aq~ (fig. 9, curve b). These
POWER
(
P MW
)
0.75
1
1.5
I
I
I
o
<~ o ~10%E G 01 )-
--15 I/~ < 1" --30 IZ
-15° ~
I--45 -I O. I-
X -10" ~
D
n
,,E, 5%-
z W
-5 ° ~
v
I
I _Q
a
2'5 a,b_
~o
ACCEPTANCE
7'5 (z~01/2rl
en°/o)
Fig. 9. Computed phase extension (curve a) and energy spread (curve b) at the output of ALS buncher for different acceptance values. Output phase of the bunch for different rf power (or accelerating field) values.
E MV/m 5-
3
!
/
4 O
2
I
1
O
I , , I, to I
100 28
160
I
_o, zL
30
500
synchronous
I
900
(ram)
buncher
5 4
b
3
,
I !
'
2 1
O
]
,
,'oo • 4.,
,5
,,
,,
,o
~2
3oo/,oo 24
2,
,
,
,'oo
Z (ram)
,oo
synchronous
buncher
Fig. 10. Accelerating field values along z-axis for travelling wave buncher designs (a) and (b) (discussed in text) and including the use of prebunching. Lengths of the modulation cavity, of the drift space, when prebunching is used, and of the first cells of the structure are given. The dephasing between adjacent cells of the two structures is ~zt.
344
D. T R O N C
of its phase extension. But the energy spread occurs afterwards, when the bunch is synchronous with the accelerating field and near its crest. Then: A V0 __ k ( c o s q g l _ c o s 9 2 )
Vo = 2k sin ~PI +-@2 sin ¢Pl-9/02 2 2
~,
--
½k(Aq~)2,
with qh = 0 (one side of the bunch at the crest) and tp2 = +Acp. 4) The bunching occurs around an output mean phase ~Po which changes with the level of the accelerating field E so that the output mean energy of the bunch is kept constant (fig. 9, curve c). For Saclay design ~/P cos ~oo = de=0.86. This explains why, when for other applications a variable energy accelerator is needed, it is necessary to use a short bunching structure followed by a synchronous structure and to adjust the phase shift between them.
7. Designs of electron injectors A long cavity for which the mean output energy is close to the maximum is used: its length is 26 m m in the conditions of fig. 6. The field's bell shape inside this cavity requires in practice the use of a greater length for comparable results. At the end of such a cavity the bunch is ahead of the crest of the field and it will be necessary to shift the bunch behing the crest, in the phase bunching region. This is done through the help of the phase variation between this first long cell and the following cell together with an asynchronous law of phase chosen for the trajectory of the bunch along the three or four first cells.
For a given mode of operation with a given dephasing between cells this is achieved by proper selection of the lengths of these cells, which are slightly shorter than required for synchronism for the average energy value at the output of the long cell. This corresponds to the synchronism for an energy of 40 keV at the input of the long cell. The 2n/3 mode of operation is selected. Fig. 10 gives the field values along the z-axis together with lengths of cells for the designs discussed below, including the prebunching which can be used if improved results are needed. The entrance of this premodulation cavity is taken as origin. The field values of the first design (a) correspond to a travelling wave structure with coupling irises of 18 m m for 0.7 M W of rf power or 22 m m for 1.4 M W for 3 G H z and iris thickness of 3 ram. The results obtained below will be more easily understood if a lens representation for the bunching process is used. Fig. 11 gives such an optical analogy for several designs. Monoenergetic input electrons correspond to parallel rays, before the first lens. The axis corresponds to the "central" trajectory around which bunching occurs and the two optical rays correspond to two electrons representative of the bunching process. They are chosen well inside the phase acceptance domain at a short distance from the "central" electron. They usually "cross" each other after several cavities. (This optical model is valid only for a limited part of the phase acceptance domain as outer electrons have a different behaviour: they are less compressed and usually do not "cross" each other.) A bunching/accelerating iris structure is represented by two successive convergent lenses (2) and (3) in fig. 11. The lens (2) represents either the bunching
0
b
1
-0.5-
¢
I
I
-4
INPUT
Fig. 11. Lens representation for bunching process in several different designs (see text).
I
I
-2
PHASE
RAD.
Fig. 12. Output phase vs input phase without prebunching and without (curve a) or with (curve b) a 28 m m long cavity. See fig. l l a .
ELECTRON
INJECTORS
FOR LINEAR
effect of the first "synchronous" cells of a natural buncher or the effect of a first " l o n g " cell alone in other designs. The phase domain extension valid for the analogy used is larger with a long cell. Crossing of central electrons occurs inside the bunch and the lens (3) represents the bunching effect of the remaining cells of the structure where electrons are behind the crest of the wave, in the convergent region. Electrons do not cross each other later as the increase of energy "freezes" the bunch. When prebunching is added as in fig. 1 l b and c a convergent lens (1) accounts for the presence of the modulation cavity. For a " n a t u r a l " buncher the overall behaviour depends strongly on the distance between this prebunching cavity and the iris structure. In most cases, its value must be different from the " b e s t " drift space value as defined for prebunching alone. Then the design problem for an injector corresponds to the proper choice of the lenses, positions and convergences. The convergence depends on the phase law followed by the bunch center for a given accelerating field level. 1) Fig. 12 gives the output phase (for z = 860 m m and an energy of 2.9 MeV) versus the input phase (z -- 170 mm) for the field values of fig. 10a, with or without a first long cell. There is no prebunching. The bunching is excessive and the electrons cross each other leading to a negative slope of the two phase diagrams. The crossing occurs around the third cell, early in the accelerating process. A~oo/d~o ~= 0 . 2 5 without the long cell, Aq~o/A~Pl = 0.13 with a long cell. These two cases correspond to fig. 11 a but the lens (2) has a lower convergence when it corresponds to the beginning of the structure including a first long cell, and this explains the better overall compression value. The
345
ACCELERATORS
two phase laws were chosen to give a similar number of accelerated electrons. A further decreasing of the convergence would be obtained at the expense of this number.
2) Fig. 13 gives the output phase (z = 860 mm) versus the input phase (z = 0) for an effective modulation of -t-5 kV and for an optimized drift space value of 160 mm. This value is greater than the best compression value of 120 m m for prebunching alone as the excessive convergence of the accelerating structure must be corrected. This choice corresponds to fig. l l c to be compared to fig. l l b which would give a worse result on the final bunch extension than without prebunching even if the number of accelerated electrons has increased. Without a long cavity (fig. 13, curve a) the bunch has a phase extension of 13 ° (for 230 ° input) with a rather uniform density at the center and two maxima of density at its extremities. With a long cavity the bunching of a// the accelerated electrons is comparable (fig. 13, curve b) but the bunch is very different and one half of the accelerated electrons are very strongly compressed. Furthermore variations of prebunching parameters are much less important. If a chopper is included in the design before the modulation cavity a bunch of a few degrees can be expected (90 ° input inside 1° output). Space-charge effect has been computed as the long drift space together with the very strong bunching for half of the r~ 0 < rr Ill m
< z
e-o.5 I-
Io
-1
-6
-5 J
. . . . . .
-3
-0.5
-4 I
-2 INPUT
I
]
I
I
I
-5
-4
-3
-2
-1
INPUT
PHASE
-0 HAIti.
Fig. 13. O u t p u t p h a s e vs i n p u t p h a s e with p r e b u n c h i n g without (curve a) or with (curve b) a long cavity. See fig. l l a .
-3 [
T -- -- -- r
-2 I
T
-1 PHASE
I l
0 HAD.
Fig. 14. O u t p u t p h a s e vs i n p u t p h a s e without p r e b u n c h i n g for design o f fig. l l b . C o m p a r i s o n o f curves a a n d b shows the i m p r o v e m e n t obtained with a long cavity. Curves c a n d d show that the length o f the long cell or the field level are n o t critical for the b u n c h i n g quality (only the o u t p u t average p h a s e changes). Lower scale o f i n p u t p h a s e corresponds to curve a, upper scale corresponds to curves b, c, d.
346
D. T R O N C
electrons increases its effect. For a beam diameter of 2.5 m m and a gun current of 50 mA, 12 mA (or 90 ° input) are bunched well inside 2 ° . 3) The level of the field decreases to three-quarters of its preceding values and fig. 14 compares the output phases at an energy of 2.5 MeV versus the input phase with and without a first long cell. The long cell has been lengthened by 4 m m and the lengths of the following cells increase more slowly (fig. 10b). The bunching is now optimized. 60% of the output electrons are inside a 4 ° bunch corresponding to an initial extension of 130 ° (fig. 14b). Without the long cell, crossing occurs again (fig. 14a). Sensitivity to variation of parameters has been analyzed for this design: in fig. 14c the long cavity is reduced by 3 mm, in fig. 14d the fields are increased by 22%. This design leads to a very simple injector, useful for example for medical or industrial applications without prebunching and with no provision for adjustment of electrical parameters. There is only a phase adjustment between the bunching structure and the following synchronous structure if a high energy is needed when rf power is increased. Similar results can be obtained with a biperiodic or a triperiodic standing wave structure. 4) A premodutation cavity with its drift space is added to these structures. The drift space is taken equal to 75 m m with the long cavity and 112 m m
d rr tu
0
a" IX
I-
~
-O.E
-1
I -5
I -4
I -3
I -2 INPUT
I -1 PHASE
I -0 gAD.
Fig. 15. O u t p u t p h a s e vs input p h a s e with p r e b u n c h i n g for design o f fig. 1 lb. C o m p a r i s o n of curves a a n d b shows that the drift space choice (or the modulation) is critical without a long cell. C o m p a r i s o n o f curves c a n d d shows that p r e b u n c h i n g parameters are n o t critical with a long cell.
TABLE 3 Space-charge effect for design o f fig. l i b with long cavity a n d prebunching.
Injected current I0 (mA)
Accelerated current In (mA)
0 50 100 200
0 38 75 150
B u n c h extension (°) 0.75 la 2.5 MeV
0.75 Is 4.7 MeV
0.5 Is 4.7 M e V
8.2 6.2 7.0 7.9
4.6 5.3 6.5
2.3 2.8 4.2
without it, for a modulation of + 4 kV. Fig. 15 gives the corresponding output phases at a 2.5 MeV level versus the input phase before the modulation cavity. When prebunching is added to a " n a t u r a l " buncher, results become comparable to performances of a buncher with a long cavity but without prebunching (fig. 15a). However, this system is very sensitive to the drift space length (and to space-charge effects which require a variation of this parameter), to the phase adjustment between premodulation field and the structure field and to the level of premodulation. In particular if the drift space is 75 m m instead of 112 m m (or if the premodulation is decreased) the bunching is destroyed (fig. 15b). With prebunching added to the buncher with a long cavity the number of accelerated electrons is increased. The drift space length (or level of premodulation) is not at all critical as shown in figs. 15c and d, this last figure corresponding to a drift space of 112 mm. The convergence has been increased but the crossing occurs far in the structure and the space-charge has a favourable effect. Space-charge effect was computed for a beam of 2.5 m m diameter between 0 and 200 mA and results are given in table 3. A chopper added to this design will give a bunch of 20 mA and 1° to 2 ° phase extension for a high performance linear accelerator. The advantages on other designs are the lower cost of the gun and its modulator together with low sensitivity to premodulation level and phase misadjustments. References 1) D. Tronc, Electron p r e b u n c h i n g with space-charge effects, 1971 Particle Accelerator C o n f . - I E E E Trans. Nucl. ScL NS-18, no. 3 (1971) 550.
E L E C T R O N I N J E C T O R S FOR L I N E A R A C C E L E R A T O R S z) K. R. Crandall and C. R. Emigh, MP4/KC2, part B (1967). 3) Patent 70 39.261. 4) H. Leboutet and D. Tronc, Improvement of the bunching in injectors for electron linacs, 1971 Particle Accelerator Conf. (1971) p. 558. 5) K. B. Mallory and R. H. Miller, On non-resonant perturbation measurements, IEEE Trans. MTT (1966) 99. 6) B. Epsztein and D. Tronc, Phase measurement along linac sections by a resonant method, 1966 Linac Acc. Conf. (Los Alamos, 1966)p. 198.
347
7) p. Brunet and X. Buffet, Electron injectors, B.2.1., in: Linear accelerators (eds. P. Lapostolle and A. Septier; NorthHolland Publ. Co., Amsterdam, 1970) p. 247. 8) j. Haimson, A low emittance high duty factor injector linac, 1971 Particle Accelerator Conf. (1971) p. 592. 9) E. Durand, Eleetrostatique, vol. I (Masson, Paris) p. 333. 10) G. Azam, A. Bensussan, H. Leboutet and D. Tronc, ALS, caract6ristiques du faisceau d'61ectron, l'Onde Electrique (Dec. 1969) 1136.