Khodnevych Vitalii
[email protected]
CLIO accelerator simulation in ASTRA This report present simulation of CLIO accelerator in ASTRA code. Main parameters are summarised. To optimize bunch length study of phase is done. The program ASTRA tracks particles through user defined external fields tacking into account the space charge field of the particle bunch. The tracking is based on a non-adaptive Runge-Kutta integration of 4th order [1]
Magnetic fields To keep particles on orbit, several solenoids and quadruples was installed. Field of magnets is increased according to increase of particles energy. For low energy solenoids are fine, but for high energies quadruples are more applicable. For ASTRA simulation longitudinal on-axis field Bz is important. The transverse field components is calculated from the derivatives of the on-axis field [1]. To calculate on-axis field next formula is used [2]: Bz =
iξ+ ξ µni h √ 2 2 ξ + a2 ξ−
where ξ± = z ± L2 , µ – permeability, a – coil radius, L – coil length, n – number of turns per unit lenght, i – current in each filament. In script file of ASTRA this field is renormalized by maximum value given in [3]. Example of solenoid fields are presented on fig. 1 Solenoide section 0.25
0.08
0.2
0.06
0.15
Bz, [T]
Bz, [T]
Bobine B1 0.1
0.04
0.05
0.02 0 −3
0.1
−2
−1
0 z, [m]
1
2
0 −4
3
(a) Field in B1 solenoid
−2
0 z, [m]
2
4
(b) Field of solenoid (accelerating) section
Figure 1: Examples of field in diiferent parts of CLIO accelerator Quadruples are also present in CLIO accelerator, but they are out range of interest. Profile of magnetic field presented on fig 2, which is in agreement with previous calculation:
1
Profile of magnetic field Bz
Bz, [T]
6
0.1
4
0.05
2
0
200
400 Z, [cm]
FWHM, [mm]
X Y
0.15
600
(a) Magnet field along the accelerator with transverse bunch width
(b) Magnet field along the accelerator [3]
Figure 2: Profile of magnetic field
Gun The gun is a classical Pierce gridded gun with a thermoelectric dispenser cathode [4]. This gun have quite complicate geometry, so in ASTRA simulation was used simplified model of it with saving all out parameters (emmitance, x-y distribution, bunch length, energy etc). To generate initial distribution program generator is used (additional program to Astra). Main parameters are follow: Cathode=T – particles are emitted from cathode, so temporal distribution is generated rather than Z. Q total=1.2E0 – total charge is 1.2nC Dist z=’plateau’, Lt=0.8E0, rt=0.1E0 – temporal distribution (see fig. 3) is plateau with length 0.8ns and rising edge 0.1 ns. Pz for all particles equal zero. In XY plane particles are distributed by Gaussian distribution with sigma equal 2 mm. Initial time distribution at cathode 0.03
150
Probability
0.025 100
0.02 0.015
50
0.01 0.005 0
0
0
0.1
0.2
0.3
0.4
0.5
0.6
t, ns
−0.4
−0.2
0 0.2 Time, [ns]
0.4
0.6
0
(a) Time distribution at cathode
0.02
0.04
0.06
0.08
0.1 0.12 z, m
0.14
0.16
0.18
0.2
(b) Longitudinal distribution at exit of gun
Figure 3: Temporal distribution Emittance is 15πmm × mrad Dist x=’gauss’, sig x=2.0E0 Dist px=’g’, Nemit x=15.0E0, Same set fot Y.
2
8
15
30
6
Y, [mm]
2
20
0
15
Py, [keV/c]
25
4
−2 10
−4
−8 −8 −6 −4 −2
0 2 X, [mm]
4
6
8
10
30
5
25 20
0
15 −5 10 −10
5
−6
35
−15 −15
0
(a) XY distribution
5 −10
−5
0 5 Px, [keV/c]
10
15
0
(b) Px Py distribution
Figure 4: Distributions of particles at cathode Parameter Total charge (Q total) Emmision time (Lt) Cathode diameter Norm. emmitance Energy of electrons Cathode-Anode dist.
Value 1.2 nC 0.9 ns 8 mm 15πmm × mrad 90 keV 24 mm
Source [6] [4] [4] [4],[3],[5] [4],[5] [4],[5]
To simulate gun, cavity with dc field is created. FILE EFieLD(1) = ’GUN.dat’, C pos(1)=0, C higher order(1)=T, MaxE(1)=-3.75, Phi(1)=0.0, And at the exit of gun apperture with 8 mm diameter is installed &APERTURE LApert=T, File Aperture(1)=’Rad’, Ap Z1(1)=-0.001, Ap Z2(1)=0.0, Ap R(1)=4, !iris des canon / Cross section of parameters exactly after aperture is not very informative as part of electrons still emitting from cathode. After aperture distributions presented on fig.5. 8
90.25
40
20
6 90.125
30
15
2 0
Ek, keV
Y, [mm]
4
20
−2 −4
90 10 89.875
10
5
−6 −8 −8 −6 −4 −2
0 2 X, [mm]
4
6
8
89.75 0.03 0.06 0.09 0.12 0.15 0.18 0.21 z, m
0
(a) XY distribution
0
(b) Dependence Pz from on-axis particle position
Figure 5: Distributions of particles after the gun
3
Bunching Subharmonic buncher The subharmonic buncher is a stainless-steel reentrant cavity MHz i.e. the 1/6th subharmonic of the fundamental frequency Parameter Value Height of the gap 19mm (18.6 mm) Working frequency 499.758 MHz Voltage 30 kV Phase 180 deg. Mode TM01 Bunch length before SGB ˜1ns ˜0.2ns (180 ps) Bunch length after SGB Energy before FB γ = 1.195, β = 0.548 Pulse duration before FB ¡=200 ps Energy spread FB ∆γ/γ = 4.9e − 2
in the mode TM01 at 499.758 of the accelerating cavity [6]. Source [3] ([5] p.62) [3] p.41 [3] p.39; [5] p.62 [4] [3] p.39; [5] p.62 [3] p.39 [3] p.39 ([5] p.61) [3] p.45 [3] p.45 [3] p.45
Important role in bunch compression play correct phase and maximum field of the cavity. So 2D scan is requred. Main criterion is to get bunch optimal for further bunching and acceleration. On figure 6 presented amplitude of the bunch, FWHM, FW0.1M and relative velocity (β) as function of phase and field amplitude.
150
0.1 250 0.08
200
0.06
150
2000
100
100
0.04
50
0.02
1500
50 0
0.12 300
phi, [°]
phi, [°]
Maximum of convolution with 200ps window, [a.u.] 4000 300 3500 250 3000 200 2500
1000 0 1
2 3 Emx, [Mv/m]
4
1
2 |∆β|
3
4
(b) Relativistic |β − 0.548|, where 0.548 from [3]
(a) Bunch charge FW0.1M, [ns]
FWHM, [ns] 0.9
0.8
300
300
0.7
0.8 250
0.7
200
0.6
150
0.5
100
0.4
100
50
0.3
50
phi, [°]
phi, [°]
250
0
2 3 Emx, [Mv/m]
0.6
200
0.5
150
0.4 0.3 0.2 0.1
0.2 1
0
0
4
(c) Full width at 10% of maximum
1
2 3 Emx, [Mv/m]
4
(d) Full width at half of maximum
Figure 6: Dependence of bunch parameters from phase and field amplitude As there are several parameters by wich bunches are selected (fwhm, fw0.1m, amplitude etc), so there is need to maximise amplitude and minimise bunch width. Big fw0.1m (long tails) will produce satellites. So I choose minimum of fw0.1m, which is close to maximum of 4
amplitude and minimum of fwhm. All measurments are made at the entance of fundamental buncher. So the phase is 126 degree and field is 2.56 MV/m. So at phase of 126 degree bunch distribution is presented on fig. 7 FWHM=87.87 ps 500
Amplitude, [a.u.]
400 300 200 100 0 −0.2
−0.1
0 t, [ns]
0.1
0.2
(a) Longitudinal distribution
(b) Pz vs. ∆φ distribution (accordig to reference particle)
Figure 7: Distributions of bunch at entrance of FSW buncher Bunch distribution near working point is presented on fig.8. 1200 φ=72 deg.; Emax=2.4 MV/m φ=108 deg.; E
max
φ=144 deg.; Emax=2.4 MV/m 600
φ=126 deg.; E
φ=108 deg.; E
=2 MV/m
φ=108 deg.; E
=2.4 MV/m
max
1000
=2.4 MV/m
Amplitude, [a.u.]
Amplitude, [a.u.]
800
=2.56 MV/m
max
400
800
max
φ=108 deg.; Emax=2.8 MV/m φ=126 deg.; E
=2.56 MV/m
max
600 400
200
200 0
−0.6
−0.4
−0.2 t, [ns]
0
0.2
−0.6
(a) Longitudinal distribution with varying phase
−0.4
−0.2 t, [ns]
0
0.2
(b) Longitudinal distribution with varying field
Figure 8: Longitudinal distribution of bunch near working point
5
Fundamental buncher The fundamental buncher is a copper triperiodic, S-band standing wave structure. It is composed of 3 wavelength, slightly matched to the beam velocity (0.92, 0.98 and 1 lambda) of the buncher [7]. The role of the 3 GHz buncher is to complete the compression phase current pulses initiated by the cavity subharmonic 500 MHz and also to give the micro-particles pack enough energy to make them ultrarelativistic [3]. On figure 9 field in fundamental buncher is presented. It is used in ASTRA simulation and field of this buncher from [3]. Field in fundamental buncher 1
Ez
0.5
0
−0.5
−1 0
0.1
0.2 Z, [m]
0.3
Figure 9: Field in fundamental buncher
Parameter λ0 Frequency No load energy Useful length dE/dz Out energy Out pulse width
Value 10 cm 2998.55 MeV 4 MeV 0.35 m 22 MeV/m ≥2.84 MeV ≤15 ps
Source [3] p.45 [3] p.45 [3] p.46; [7] [7];[6] [6] [3] p.53 [3] p.53
As subharmonic buncher, fundamental buncher also require phase study. On fig. 10 are presented most important results. Maximum of convolution with 15ps window
0.035
4000
FWHM FW0.1M
3000
bunch length, ns
Amplitude, [a.u.]
0.03
2000
1000
0.025 0.02 0.015 0.01 0.005
0 0
100
200 phi, [°]
0 0
300
100
200 phi, [°]
300
(a) Dependence of bunch amlitude from phase (b) Dependance of full width at half and 10% of FSW buncher of maximum from phase of cavity
Figure 10: Phase study plots for FSW buncher 6
FWHM=0.9224 ps
Amplitude, [a.u.]
250 200 150 100 50 0
−5
0
5 t, [ns]
10
15 −3
x 10
(b) Pz vs. z distribution of bunch
(a) Longitudinal distribution of bunch
Figure 11: Distributions of bunch at entrance of accelerating cavity for phase of FSW buncher 210 degree For this case most aplicable phase is 210 degree. On fig 11 bunch distribution is presented. If reader is curious in energy distribution of resulted bunch, he can find answer on fig. 16b. For this subsection all distrubution are taken at the entrance of accelerating cavity. Energy distribution in bunch
250
200o o 210 240o
100 Amplitude, [a.u.]
Amplitude, [a.u.]
200
120
150 100
80 60 40
50 20 0
0
0.01
0.02
0 3.2
0.03
t, [ns]
(a) Longitudinal distribution of bunch near working point
7
3.4
3.6 3.8 Pz, [MeV]
4
(b) Energy distribution in bunch
4.2
Comparison with PARMELA For this subsection all distrubution are taken at the exit of fundamental buncher.
Loc.= 118cm; FWHM=7.4 ps
Amplitude, [a.u.]
2000
1500
1000
500
0 −400
−200
0 ∆ φ, [deg]
200
400
(a) Longitudinal distribution of bunch
(b) ...
Amplitude, [a.u.]
Loc.= 118cm; FWHM=7.4 ps
1500
1000
500
−60
−40
−20 ∆ φ, [deg]
0
20
(a) Longitudinal distribution of bunch
(b) ...
8
Energy distribution in bunch 500
Amplitude, [a.u.]
400 300 200 100
3.4
3.6
3.8 4 Pz, [MeV]
4.2
4.4
(a) Longitudinal distribution of bunch
(b) ...
(a) Longitudinal distribution of bunch
(b) ...
9
The accelerating cavity The cavity is a constant gradient S band travelling wave disk-loaded structure. The cavity is surrounded with a set of solenoidal coils which give a continuous axial field adjustable up to 0.2 Tesla [7]. Field in acceleration cativity
Ez, [a. u.]
1
0.5
0
−0.5 0
0.05
0.1 Z, [m]
0.15
0.2
Figure 17: Field in accelerating cavity (field amplitude of one RF period plus the input and output coupler cells) Parameter frequency length mode no load energy cell number
Value 2998.550 4.5m 2π/2 78 MeV 135
Source [7] [7] [7] [7] [3]
Same phase study are done for accelerating cavity. Maximum field in cavity is 22 MV/m. Phase 310 degree give smallest bunch length (fig. 18b), but egergy spread for it is quite big (fig. 18e), so phase 20 degree is choosen. Distribution of bunch is presented on figure 19. Spectrum of the profile presented on figure 22.
10
Maximum of convolution with 15ps window
0.04
2500
FWHM FW0.1M Bunch length, ns
Amplitude, [a.u.]
2000 1500 1000 500 0 0
100
200 phi, [°]
0.03
0.02
0.01
0 0
300
100
200 phi, [°]
300
60
100
50
80
40
60
T, [%]
E, [MeV]
(a) Dependence of bunch amplitude from (b) Dependance of the full width at half and phase of accelerating cavity 10% of maximum from phase of cavity
30
40
20
20
10 0
100
200 phi, [°]
0 0
300
100
200 phi, [°]
300
(c) Dependence of the bunch energy from (d) Dependance of the transmission from phase of accelerating cavity phase of cavity 1
0
10
0.8 −1
∆ γ /γ
∆ N/N
10
0.6 0.4
−2
10
0.2 0 0
−3
10
0
100
200 phi, [°]
300
100
200 phi, [°]
300
(f) Dependance of the number of particles in (e) Dependence of the bunch energy spread bunch 2% energy spread to number of partifrom phase of accelerating cavity cles in bunch from phase of the cavity
Figure 18: Phase study plots for accelerating cavity
11
Loc.= 710cm; FWHM=2.3 ps
Amplitude, [a.u.]
1200 1000 800 600 400 200 0 −0.5
0 t, [ns]
0.5
(a) Longitudinal distribution of bunch
(b) Pz vs. t distribution of bunch
Loc.= 710cm; FWHM=2.3 ps
Amplitude, [a.u.]
1200 1000 800 600 400 200 0 −0.01
−0.005
0 t, [ns]
0.005
0.01
(c) Longitudinal distribution of bunch (zoomed)
(d) Pz vs. t distribution of bunch (zoomed)
Figure 19: Distributions of bunch at the exit of accelerating cavity for 20 degree phase
12
250
10 5
200
Pz, MeV
Amplitude, [a.u.]
15
40o o 20 o 0
300
150
0 −5
100
o
40
20o
−10
50
o
0
−0.01 −0.005
0 0.005 t, [ns]
−15 −0.05 −0.04 −0.03 −0.02 −0.01 t, [ns]
0.01
0
0.01
(b) Pz vs. t distribution of bunch
(a) Longitudinal distribution of bunch
40 20o 310o 210o
600
400
200
0
20o 310o 210o
20 Pz, MeV
Amplitude, [a.u.]
800
0 −20 −40
−5
0 t, [ns]
5
−60 −0.1
10 −3
x 10
(c) Longitudinal distribution of bunch
−0.05
0 t, [ns]
0.05
0.1
(d) Pz vs. t distribution of bunch
Figure 20: Distributions of bunch at the exit of accelerating cavity for 3 phases
13
Energy distribution in bunch
Energy distribution in bunch 300
o
250
310
60
210o
Amplitude, [a.u.]
Amplitude, [a.u.]
40o 20o 0o
20o
70
50 40 30 20
200 150 100 50
10 30
35
40
45 50 Pz, [MeV]
55
0 52
60
(a) Energy distribution of bunches
54
56 58 Pz, [MeV]
60
(b) Energy distribution of bunches
Energy distribution in bunch
Amplitude, [a.u.]
600 500 400 300 200 100 59
59.5 60 Pz, [MeV]
60.5
(d) PARMELA [5]
(c) Energy distribution of bunch
Figure 21: Distributions of bunch at the exit of accelerating cavity
6
2.5
x 10
4
10
Amplitude, [a.u.]
Amplitude, [a.u.]
2 2
10
0
10
o
20 −2
310o
10
1.5 1 0.5
210o 0.05
0.1 λ, [mm]
0 0
0.15
2
4
6
8
10
λ, [mm]
(a) Spectrum of profile in (0,0.2)mm region
(b) Spectrum of profile in (0,10)mm region
Figure 22: Spectrum of profile (Black – 20o , Red – 310o , Blue – 210o phase )
14
4
x 10
85
8
80
6
75
T, [%]
FWHM, [ns]
10
4
70
2
65
0 0
200
400 Z, [cm]
600
60 0
800
200
400 Z, [cm]
600
800
(a) Dependence of the bunch width from distance(b) Dependence of the transmissivity from distance in accelerator in accelerator 2
10
1
E, [MeV]
10
0
10
−1
10
0
200
400 Z, [cm]
600
800
(c) Dependence of the bunch energy from distance in accelerator
Figure 23: Some dependences from distance
15
Bibliography [1] Klaus Floettmann, A Space Charge Tracking Algorithm Version 3.0, DESY, Germany, October 2011(Update April 2014) [2] Edmund E. Callaghan, Stephen H. Maslen NASA Technical note D-465. The magnetic field of finite solenoid, Washington, USA, October 1960 [3] Rapport d’etude du projet de laser a electrons libres sur accelerateur lineaire HF 3 GHz: CLIO,LAL/RT-89/04 [4] J.C.Bourdon & comp. Commissioning the CLIO injection system, NIMPR A305(1991) 322328 [5] Francois GLOTIN Le laser a electrons libres CLIO et sa structure temporelle These, Univ. Paris VII, 1994 [6] R. Chaput & comp. Optimisation of the FEL CLIO Linear Accelerator [7] J.C.Bourdon & comp. CLIO: Free Electron Laser in ORSAY
16
