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Study for a beam bunching system at LNS
158
Nuclear Instruments and Methods in Physics Research 220 (1984) 158-160 North-Holland, Amsterdam
STUDY FOR A BEAM BUNCHING Luciano CALABRETTA
SYSTEM
AT LNS
and Emilio MIGNECO
lstituto Nazionale di Fisica Nucleare, Laboratorio Nazionale del Sud, C. so Italia, 57, 95129 Catania, Italy
The injection of a beam from a tandem accelerator into a superconducting cyclotron requires the production of very short beam bunches. A simple formalism for the analysis of a tandem beam bunching system consisting of low energy and high energy buncher is presented. The random energy spread, the non linearity of the buncher wave-form, the aberration due to the electric field distribution in the gaps and the stripper energy spread are simulated with a computer code. Our planned LE buncher and its theoretical performance are presented.
1. Introduction
The heavy ion facility at LNS will consist of an SMP tandem injecting into a K = 800 superconducting cyclotron. In order to acheive the desired energy resolution of 10 3 on the final energy of the beam, a bunching system producing ion beam pulses within a phase spread of + 1.5 °, corresponding to At = 170-560 ps for a cyclotron frequency of 15-48 M H z is required. Moreover as high an efficiency as possible is always demanded (e.g. ~ >~ 60%). It is well known [1,2] that the above mentioned performance cannot be obtained with a single stage buncher, because of non linear effects such as time aberrations and stripper energy spread. We have, therefore, studied a double stage system consisting of a primary buncher placed after the tandem
preinjector (LE buncher) and a rebuncher placed between the tandem and the cyclotron. In fig. 1 the coupling line between the two accelerators and the position of the two stage bunching system are shown. The LE buncher will produce a time focus at the tandem stripper in order to minimize the longitudinal phase space (z, pz) growth produced by the energy straggling in the stripper, while the rebuncher will ensure the required bunch length at the cyclotron stripper. We have analyzed the main characteristics of the bunching system using a matrix formalism. Moreover the efficiency has been calculated using a computer code that includes non linear effects. 2. Matrix formulation
The coupling line between the tandem and the cyclotron produces an achromatic double waist at the
I
Fig. 1. Layout of the coupling line between the tandem and the cyclotron. Injection elements are D (dipole), q and Q (quadrupole), S (slit).
0167-5087/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
159
L. Calabretta, E.M. Migneco / Study for a beam bunching system at LNS rebuncher position and also achromatic transport to the cyclotron stripper. Therefore the longitudinal phase space is decoupled from the transverse phase space and, following the Brown formulation [3], the beam bunch can be represented by a 2 × 2 matrix having the form: [Oo] = '[ 12
r01oSo ]
t ro/oSo
8oz
,
(1)
where I 0 is the half length of the pulse, 80 = d p / p is the hwhm of the relative m o m e n t u m distribution, and r o is the correlation coefficient (r o = 0 before the LE buncher). It is also know that the energy modulation E m required for the bunching of non relativistic particles is given by [4]: E m = - 2 E i l / F for - l o ~< l ~< l 0, E i being the energy and l the position of the particles. F is the effective distance between the buncher and the time focus defined as in ref. 1. An ideal buncher can then be represented by the following transformation matrix: [Bll=
[ - 11/ F 1
01.
(2)
We can also describe a drift length including acceleration by the matrix [5]:
ZPlfG1],I/G1
[£pl]=[0G~
(3)
where A°I is the effective distance as before and G1 is the ratio between the energy at the end and at the entrance of the drift. The transfer matrix from the LE buncher to the stripper of the tandem can then be written as [ R ] = [.Lal ][B1], and the beam matrix at the tandem stripper is [a t 1= [R ][ o0 ][ k ]; we can easily show from this, that the condition for a time focus at the terminal stripper is F1 = Aal. It is therefore possible to represent the beam after the stripper by the following matrix:
o]
[oil =
82
,
(4)
within 12 =~'12G182 + Al E where AI w is introduced to take into account the wave-form aberration; and 82-
A E s t 12 1~°2 +( 2E t ] , (G1LPl) 2
(5)
where A Es t is the stripper energy straggling. The beam matrix at the cyclotron stripper is [ % ] = [Sl[o,][Sl, where the transformation matrix is [ S ] = [L3][B2][.oq°2]. [ c~a2] and [L3] are the drift matrices of the t e r m i n a l - r e b u n c h e r r e g i o n a n d of the rebuncher-cyclotron stripper region respectively; [B2] is the rebuncher matrix with focal length F2. The length of the pulse at the cyclotron stripper is: l c = (o.cl,) 1/2 = (S?112 .q- S7287) 1/2. To obtain the minimum pulse length we may put $12 = 0 or Sal = 0. The condition $12 = 0 is fulfilled when the focal length of the rebuncher is
F2 = ( L3Aa2G2fG2 ) / ( L3 + c.La2G2G ~ ) and in this case the pulse length can be written as:
lc = ltLa/(G2.~
)
or
Aq~¢=Aq, t L 3 / ( . C . ~ G 2 G ~ ).
The final pulse length is independent of the energy spread introduced by the terminal stripper, but in order to fulfil the cyclotron requirement Aq~c = + 1.5 °, a pulse length Aq,t = + 4 ° - 1 0 ° at the tandem stripper is required. For ions with mass A < 60 this corresponds to a pulse length less than 1 ns, which is a rather difficult task to achieve especially when an efficiency higher than 60% is demanded. Under the other condition $11 = 0, fulfilled when F 2 = L3, the pulse length at the cyclotron stripper is:
l~ = 8 t L 3 / G 2
(6)
and depends only on the m o m e n t u m spread at the tandem stripper. Thus, the pulse length delivered by the LE buncher can be as large as + 3 0 ° of the rf phase of the rebuncher.
Table 1 Characteristic parameter used for the calculations of the binding system efficiency. V1 and V2 are peak voltages at r = 0 in the first and second tube respectively. Ion
Ei
q,
(keY) 12 C a) 16 O a) 2 8 5 i a)
63Cu 127I
197Au 13s
150 150 200 200 300 300 350
2 2 3 4 7 11 11
Ef/h
Pc (MHz)
~b (MHz)
AEst (keY)
Era (keY)
A~be°
V1 (kV)
V2 (kV)
Vr (kV)
*1(%)
(MeV/amu) 100 100 100 65 40 25 20
48 48 48 40 33 24 20
16 16 16 13.3 11 12 10
2.97 4.6 4.35 6.45 6.80 35 b) 35 b)
4.53 3.92 4.4 3.4 3.8 2.7 3.7
0.73 0.95 0.83 0.88 0.54 1.21 1.11
1.290 1.100 1.225 1.070 1.590 1.200 1.550
0.650 0.490 0.5z10 0.495 0.715 0.520 0.650
110 93 74 65 60 57 61
61 60 62 67 69 56 59
a) Beam diameter at LE buncher 20-10 mm. b) Carbon foil 10 t~g/cm 2. IV. NEW ACCELERATORS
160
L. Calabretta, E.M. Migneco / Study for a beam bunching system at LNS
In table 1 we show the pulse length AO° of a set of ions at the cyclotron stripper calculated using eq. (6). TheA Est of eq. (5) has been calculated as in ref. 6 for a gas stripper, while for a solid stripper (a carbon foil of 10 /~g/cm 2) the nonuniformity of the thickness has been taken into account as in ref. 1. The results indicate that in our case the energy spread is not a serious problem even when a solid stripper is used.
3. Efficiency including nonlinear effects In order to make a more accurate study of the bunching system, a computer code of the raytracing type was used. We assumed as a first stage a "double drift buncher" of the type developed for the Oak Ridge tandem [4]. This device consists of two drift tubes of length d and d/2, the first driven at a frequency Pb and the second (located a distance D -- 50 cm from the first driven at 2v b. To obtain the maximum modulation for a given rf amplitude the drift lengths are supposed to be variable, d = 16-24 cm. The system is placed just before the LE aperture, at 2.7 m from the tandem tube entrance. We operate without gridded gaps and therefore frequencies Pb between 7 and 16 MHz, third or second subharmonic of the cyclotron frequency, are chosen to minimize the gap effects. The non-uniformities of the electric field in the gaps were taken into account using the formula obtained in ref. 4: E m ( r ) = [ 1 0 . 8 ( r / X ) 2 + 1] Em(0 ). The initial values of the position I were uniformly chosen in the range - X J 2 ~ < l<~Xi/2, where X, is the distance travelled by a particle with energy E i in one period T b = l / / F b . The momentum spread 80 = A E/2E~ has been assigned by means of a Gaussian distribution with o = ( A E s +AE~)I/2/2E,, where AE~ = 25 eV and AEi = 10-4Ei. The momentum spread due to the stripper effect A E s t / 2 E was simulated with a Gaussian distribution having the hwhm given in table 1. In order to have a sufficiently large region of linearity in the rebuncher and at the same time to minimize the rf amplitude V~, the frequency, of the rebuncher was chosen as the sixth harmonic of the frequency /)b of the double drift buncher.
The effects of long term changes ( - 10 Hz) in the tandem voltage, that can result in a mean phase shift of some ns, were not considered as they can be corrected using a proper phase control system, see fig. 1. In table 1 the bunching system efficiencies ~/for a set of ions are presented. The values shown represent the particles that arrive at the cyclotron stripper within + 1.5 ° of the cyclotron rf frequency vc and moreover with an energy spread AE/E<~ + 2 × 10 -3. The values of the efficiency for light ions such as 12C, 160 and 28Si were calculated assuming a large beam diameter (20 mm) at the position of the first drift tube and a uniform radial distribution of the beam. The efficiency values, always higher than 60%, show that for light ions the gap effects are not critical for frequencies up to 16 MHz. For heavier ions A >/180 on the other hand the gap effects make working with frequency Vb higher than 12 M H z impossible, even assuming a beam diameter of 10 mm at the first drift tube and of 6 mm at the second. This is not in fact a critical limitation because for heavier ions, a maximum final energy of 25-20 M e V / a m u is obtained with frequencies v¢ = 2v b less than 25 M H z ref. 7. We think that it is possible to improve on the results reported in table 1 for the Au and U ions by using carbon foils thinner than 10 # g / c m 2, and also by increasing the injection energy to 500 keV. In general, our calculations have shown that, for all the ions at different injection conditions, the proposed bunching system can always deliver a pulsed beam with an efficiency r/>/60% within + 1.5 ° of the rf phase of the cyclotron.
References [1] S.J. Skorka, Third Int. Conf. on Electrostatic Accelerator Technology (IEEE Press, New York, 1981) p. 130. [2] W.G. Davies, Ninth Int. Conf. on Cyclotrons and their Applications (Les 6ditions de Physique, Caen, 1981) p. 349. [3] K.L. Brown et al., Transport, CERN 80-04, Geneva. [4] W.T. Milner, IEEE Trans. Nucl. Sci. NS-26 (1979) 1445. [5] H. gasser, note G.E.P.A.S. 81-06, Strasbourg. [6] H. Schmidt-Bocking and H. Hornung, Z. Phys. A286 (1978) 253. [7] E. Acerbi et al., Ninth Int. Conf. on Cyclotrons and their Applications (Les 6ditions de Physique, Caen, 1981) p. 169.
Nuclear Instruments and Methods in Physics Research 220 (1984) 158-160 North-Holland, Amsterdam
STUDY FOR A BEAM BUNCHING Luciano CALABRETTA
SYSTEM
AT LNS
and Emilio MIGNECO
lstituto Nazionale di Fisica Nucleare, Laboratorio Nazionale del Sud, C. so Italia, 57, 95129 Catania, Italy
The injection of a beam from a tandem accelerator into a superconducting cyclotron requires the production of very short beam bunches. A simple formalism for the analysis of a tandem beam bunching system consisting of low energy and high energy buncher is presented. The random energy spread, the non linearity of the buncher wave-form, the aberration due to the electric field distribution in the gaps and the stripper energy spread are simulated with a computer code. Our planned LE buncher and its theoretical performance are presented.
1. Introduction
The heavy ion facility at LNS will consist of an SMP tandem injecting into a K = 800 superconducting cyclotron. In order to acheive the desired energy resolution of 10 3 on the final energy of the beam, a bunching system producing ion beam pulses within a phase spread of + 1.5 °, corresponding to At = 170-560 ps for a cyclotron frequency of 15-48 M H z is required. Moreover as high an efficiency as possible is always demanded (e.g. ~ >~ 60%). It is well known [1,2] that the above mentioned performance cannot be obtained with a single stage buncher, because of non linear effects such as time aberrations and stripper energy spread. We have, therefore, studied a double stage system consisting of a primary buncher placed after the tandem
preinjector (LE buncher) and a rebuncher placed between the tandem and the cyclotron. In fig. 1 the coupling line between the two accelerators and the position of the two stage bunching system are shown. The LE buncher will produce a time focus at the tandem stripper in order to minimize the longitudinal phase space (z, pz) growth produced by the energy straggling in the stripper, while the rebuncher will ensure the required bunch length at the cyclotron stripper. We have analyzed the main characteristics of the bunching system using a matrix formalism. Moreover the efficiency has been calculated using a computer code that includes non linear effects. 2. Matrix formulation
The coupling line between the tandem and the cyclotron produces an achromatic double waist at the
I
Fig. 1. Layout of the coupling line between the tandem and the cyclotron. Injection elements are D (dipole), q and Q (quadrupole), S (slit).
0167-5087/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
159
L. Calabretta, E.M. Migneco / Study for a beam bunching system at LNS rebuncher position and also achromatic transport to the cyclotron stripper. Therefore the longitudinal phase space is decoupled from the transverse phase space and, following the Brown formulation [3], the beam bunch can be represented by a 2 × 2 matrix having the form: [Oo] = '[ 12
r01oSo ]
t ro/oSo
8oz
,
(1)
where I 0 is the half length of the pulse, 80 = d p / p is the hwhm of the relative m o m e n t u m distribution, and r o is the correlation coefficient (r o = 0 before the LE buncher). It is also know that the energy modulation E m required for the bunching of non relativistic particles is given by [4]: E m = - 2 E i l / F for - l o ~< l ~< l 0, E i being the energy and l the position of the particles. F is the effective distance between the buncher and the time focus defined as in ref. 1. An ideal buncher can then be represented by the following transformation matrix: [Bll=
[ - 11/ F 1
01.
(2)
We can also describe a drift length including acceleration by the matrix [5]:
ZPlfG1],I/G1
[£pl]=[0G~
(3)
where A°I is the effective distance as before and G1 is the ratio between the energy at the end and at the entrance of the drift. The transfer matrix from the LE buncher to the stripper of the tandem can then be written as [ R ] = [.Lal ][B1], and the beam matrix at the tandem stripper is [a t 1= [R ][ o0 ][ k ]; we can easily show from this, that the condition for a time focus at the terminal stripper is F1 = Aal. It is therefore possible to represent the beam after the stripper by the following matrix:
o]
[oil =
82
,
(4)
within 12 =~'12G182 + Al E where AI w is introduced to take into account the wave-form aberration; and 82-
A E s t 12 1~°2 +( 2E t ] , (G1LPl) 2
(5)
where A Es t is the stripper energy straggling. The beam matrix at the cyclotron stripper is [ % ] = [Sl[o,][Sl, where the transformation matrix is [ S ] = [L3][B2][.oq°2]. [ c~a2] and [L3] are the drift matrices of the t e r m i n a l - r e b u n c h e r r e g i o n a n d of the rebuncher-cyclotron stripper region respectively; [B2] is the rebuncher matrix with focal length F2. The length of the pulse at the cyclotron stripper is: l c = (o.cl,) 1/2 = (S?112 .q- S7287) 1/2. To obtain the minimum pulse length we may put $12 = 0 or Sal = 0. The condition $12 = 0 is fulfilled when the focal length of the rebuncher is
F2 = ( L3Aa2G2fG2 ) / ( L3 + c.La2G2G ~ ) and in this case the pulse length can be written as:
lc = ltLa/(G2.~
)
or
Aq~¢=Aq, t L 3 / ( . C . ~ G 2 G ~ ).
The final pulse length is independent of the energy spread introduced by the terminal stripper, but in order to fulfil the cyclotron requirement Aq~c = + 1.5 °, a pulse length Aq,t = + 4 ° - 1 0 ° at the tandem stripper is required. For ions with mass A < 60 this corresponds to a pulse length less than 1 ns, which is a rather difficult task to achieve especially when an efficiency higher than 60% is demanded. Under the other condition $11 = 0, fulfilled when F 2 = L3, the pulse length at the cyclotron stripper is:
l~ = 8 t L 3 / G 2
(6)
and depends only on the m o m e n t u m spread at the tandem stripper. Thus, the pulse length delivered by the LE buncher can be as large as + 3 0 ° of the rf phase of the rebuncher.
Table 1 Characteristic parameter used for the calculations of the binding system efficiency. V1 and V2 are peak voltages at r = 0 in the first and second tube respectively. Ion
Ei
q,
(keY) 12 C a) 16 O a) 2 8 5 i a)
63Cu 127I
197Au 13s
150 150 200 200 300 300 350
2 2 3 4 7 11 11
Ef/h
Pc (MHz)
~b (MHz)
AEst (keY)
Era (keY)
A~be°
V1 (kV)
V2 (kV)
Vr (kV)
*1(%)
(MeV/amu) 100 100 100 65 40 25 20
48 48 48 40 33 24 20
16 16 16 13.3 11 12 10
2.97 4.6 4.35 6.45 6.80 35 b) 35 b)
4.53 3.92 4.4 3.4 3.8 2.7 3.7
0.73 0.95 0.83 0.88 0.54 1.21 1.11
1.290 1.100 1.225 1.070 1.590 1.200 1.550
0.650 0.490 0.5z10 0.495 0.715 0.520 0.650
110 93 74 65 60 57 61
61 60 62 67 69 56 59
a) Beam diameter at LE buncher 20-10 mm. b) Carbon foil 10 t~g/cm 2. IV. NEW ACCELERATORS
160
L. Calabretta, E.M. Migneco / Study for a beam bunching system at LNS
In table 1 we show the pulse length AO° of a set of ions at the cyclotron stripper calculated using eq. (6). TheA Est of eq. (5) has been calculated as in ref. 6 for a gas stripper, while for a solid stripper (a carbon foil of 10 /~g/cm 2) the nonuniformity of the thickness has been taken into account as in ref. 1. The results indicate that in our case the energy spread is not a serious problem even when a solid stripper is used.
3. Efficiency including nonlinear effects In order to make a more accurate study of the bunching system, a computer code of the raytracing type was used. We assumed as a first stage a "double drift buncher" of the type developed for the Oak Ridge tandem [4]. This device consists of two drift tubes of length d and d/2, the first driven at a frequency Pb and the second (located a distance D -- 50 cm from the first driven at 2v b. To obtain the maximum modulation for a given rf amplitude the drift lengths are supposed to be variable, d = 16-24 cm. The system is placed just before the LE aperture, at 2.7 m from the tandem tube entrance. We operate without gridded gaps and therefore frequencies Pb between 7 and 16 MHz, third or second subharmonic of the cyclotron frequency, are chosen to minimize the gap effects. The non-uniformities of the electric field in the gaps were taken into account using the formula obtained in ref. 4: E m ( r ) = [ 1 0 . 8 ( r / X ) 2 + 1] Em(0 ). The initial values of the position I were uniformly chosen in the range - X J 2 ~ < l<~Xi/2, where X, is the distance travelled by a particle with energy E i in one period T b = l / / F b . The momentum spread 80 = A E/2E~ has been assigned by means of a Gaussian distribution with o = ( A E s +AE~)I/2/2E,, where AE~ = 25 eV and AEi = 10-4Ei. The momentum spread due to the stripper effect A E s t / 2 E was simulated with a Gaussian distribution having the hwhm given in table 1. In order to have a sufficiently large region of linearity in the rebuncher and at the same time to minimize the rf amplitude V~, the frequency, of the rebuncher was chosen as the sixth harmonic of the frequency /)b of the double drift buncher.
The effects of long term changes ( - 10 Hz) in the tandem voltage, that can result in a mean phase shift of some ns, were not considered as they can be corrected using a proper phase control system, see fig. 1. In table 1 the bunching system efficiencies ~/for a set of ions are presented. The values shown represent the particles that arrive at the cyclotron stripper within + 1.5 ° of the cyclotron rf frequency vc and moreover with an energy spread AE/E<~ + 2 × 10 -3. The values of the efficiency for light ions such as 12C, 160 and 28Si were calculated assuming a large beam diameter (20 mm) at the position of the first drift tube and a uniform radial distribution of the beam. The efficiency values, always higher than 60%, show that for light ions the gap effects are not critical for frequencies up to 16 MHz. For heavier ions A >/180 on the other hand the gap effects make working with frequency Vb higher than 12 M H z impossible, even assuming a beam diameter of 10 mm at the first drift tube and of 6 mm at the second. This is not in fact a critical limitation because for heavier ions, a maximum final energy of 25-20 M e V / a m u is obtained with frequencies v¢ = 2v b less than 25 M H z ref. 7. We think that it is possible to improve on the results reported in table 1 for the Au and U ions by using carbon foils thinner than 10 # g / c m 2, and also by increasing the injection energy to 500 keV. In general, our calculations have shown that, for all the ions at different injection conditions, the proposed bunching system can always deliver a pulsed beam with an efficiency r/>/60% within + 1.5 ° of the rf phase of the cyclotron.
References [1] S.J. Skorka, Third Int. Conf. on Electrostatic Accelerator Technology (IEEE Press, New York, 1981) p. 130. [2] W.G. Davies, Ninth Int. Conf. on Cyclotrons and their Applications (Les 6ditions de Physique, Caen, 1981) p. 349. [3] K.L. Brown et al., Transport, CERN 80-04, Geneva. [4] W.T. Milner, IEEE Trans. Nucl. Sci. NS-26 (1979) 1445. [5] H. gasser, note G.E.P.A.S. 81-06, Strasbourg. [6] H. Schmidt-Bocking and H. Hornung, Z. Phys. A286 (1978) 253. [7] E. Acerbi et al., Ninth Int. Conf. on Cyclotrons and their Applications (Les 6ditions de Physique, Caen, 1981) p. 169.