A Simulation Study of E-driven ILC Positron Source Masao KURIKI - PowerPoint PPT Presentation

A Simulation Study of E-driven ILC Positron Source Masao KURIKI (Hiroshima University)

Introduction ● The design of the ILC positron source based on off-the-shelf components has been established. ● Further optimization was made to improve the performance and optimize the cost-effective system by, – Small beam size on target for better yield. (3.5 � 2.0 mm rms) – Lower drive beam energy for less cost. (4.8 � 3.0 GeV) – Consider only the nominal parameter. ● Booster conf i guration (lattice) is modif i ed to make the consistency. Cost Review of E-driven 24 August 2017

E-driven ILC Positron Source 5.0 GeV 3.0 GeV L-band + S-band NC S-band NC 20 of 0.48us pulses are handled with NC linacs operated in 300Hz. • 100 of 300 pulses are actually fired. • Cost Review of E-driven 24 August 2017

The beam handling and format Damping Ring tp=480 ns Positron Booster T b = 6.15 n sec 33 bunches 197 ns 81.6 ns Cost Review of E-driven 24 August 2017

Electron Driver ● 3.0 GeV Electron beam with 2.0 mm RMS beam size at the target. ● 2.4 nC bunch charge is giving 0.39 A beam loading. ● S-band Photo-cathode RF gun for the beam generation. ● 80 MW klystron-modulator drives 2 structures. ● The effective input power for each tube is 36 MW. 50 MV/tube. Cost Review of E-driven 24 August 2017

● 60 + 4 (spare) of 3m S-band TW structures for the acceleration. The energy is 3.2 GeV. ● The lattice design was based on ATF linac, 4Q + 2RF(S) up to 600 MeV, 4Q+4RF(S) for other. Lattice # of cell Cell Section length(m) length(m) 4Q+2S 6 8.0 48.0 4Q+4S 13 14.4 172.8 ● The total length is 235.2 + 20 m (RF gun + matching section). Cost Review of E-driven 24 August 2017

Positron Capture Linac 36 L-band SW structures designed by J. Wang (SLAC) for the ● undulator capture section is employed. Two structures are driven by one 50 MW klystron. ● Surrounded by 0.5 T solenoid f i eld. ● Cost Review of E-driven 24 August 2017

Beam Loading in SW Linac Single Cell Model : Simple, but not realistic ● T h e e f f e e l l d d i i n n S S W W a a c c c c e e l l e e r r a a t o o r r T 0 ) ( 1 − e ( 1 − e T 0 ) − rIL 2Q − t − t b − t V ( t )= 2 √ β P 0 r L T 0 = ω( 1 +β) 1 +β 1 +β Beam Loading RF ● T h e e v v o o l l t t a g e e b b e e c c o o me m e s s c c o o n n s s t a n n t t i i f 2 √ t b =− T 0 ln ( β P 0 ) I rL 2 √ ( 1 − I β P 0 ) V 0 = 2 √ β P 0 r L rL 1 +β Cost Review of E-driven 24 August 2017

Multi-Cell Model : More realistic Time differential of the energy of the center cell, Power flow to next cells Input Power Beam loading WG loss Power loss Power flow from next cells Cost Review of E-driven 24 August 2017

Time differential of the voltage For the intermediate cells, For the end cells, Cost Review of E-driven 24 August 2017

1 1 l i n e a r s i mu l t a n e o u s d i f e r e n t i a l e q u a t i o n s Cost Review of E-driven 24 August 2017

A can be diagonalized with a orthgonal matrix R as Because B is diagonal, the equations for V' are 11 independent linear differential equations, Cost Review of E-driven 24 August 2017

The solution for V' is The solution for V is expressed as a linear sum of the solution for V' Cost Review of E-driven 24 August 2017

Acceleration Field L=1.27 m (11 cells, L-band SW) ● R=34e+6 Ohm/m ● P 0 =22.5 MW (50MW at klystron, 5MW wave guide loss). ● 10.36 MV/tube with beta=6.0. ● Single cell Multi-cell Cost Review of E-driven 24 August 2017

R F Mo d e a n d B e a m L o a d i n g Mo d e ● The total acceleration voltage is given as sum of the RF mode and the Beam-loading mode. ● They are not identical, but the dominant mode is common (tau=1.22 us). ● The RF mode has the second dominant mode, but nothing for BL. This gives the imperfection on the BL compensation, but the effect is not large. RF mode BL mode Cost Review of E-driven 24 August 2017

Beam Loading Compensation No big difference on the no-load voltage, but 30 % less on the heavyly loaded voltage, The beam loading compensation works well. Flatness is less than 0.1%. Cost Review of E-driven 24 August 2017

Target downstream Capture Simulation Δx=254 um y 0.025 Δy=238 um 0.020 N=17115(7292) 1000 electrons on target by GEANT 4. 0.015 ● 0.010 The positron is decelerated and bunched at ● 0.005 the acceleration phase by phase-slipping. 0.000 y -0.005 Positrons with a large z (longitudinal ● -0.010 position) are not captured by the final -0.015 acceptance. This is not the case for δ . -0.020 -0.025 -0.02 -0.01 0.00 0.01 0.02 x G P T x Capture Linac exit Chicane exit 800 700 600 500 Captured d Positron 400 G 300 Electron 200 Positron 100 0 57.4 57.5 57.6 57.7 57.8 57.9 58.0 58.1 58.2 58.3 z z Cost Review of E-driven G P T s 24 August 2017

Booster A f i rst half is implemented by L-band acc. and the last half is by S-band. ● 50MW L-band Klystron drives two L-band acc. (2a = 34 mm). ● 80MW S-band Klystron drives two S-band acc. (2a = 20 mm). ● The gradient at 0.78 A (4.8nC/bunch) beam loading is assumed. ● The beam loading compensation and its accuracy determine the accelerator ● gradient. Cost Review of E-driven 24 August 2017

Beam-loading in TW Linac Transient beam-loading is compensated by Amplitude Modulation. ● A cceleration voltage by a f l at RF, ● V(no beam) loading V(with beam) RF Pulse RF Pulse V(beam loading)

B e a m L o a d i n g C o mp e n s a t i o n w i t h A M Laplace transformation of TW accelerator voltage V(s) is E ( s ) where E(s) is the Laplace transformation of applied voltage (power). E(s) is determined to cancel s (t) dependence of V(s or t).

S t e p Mo d u l a t i o n Imperfection

S a w Mo d u l a t i o n E ( t )= E 0 U ( t )+ E 1U ( t − t f )+ E 2 ( t − t f ) U ( t − t f ) t f E ( s )= E 0 s + E 1 − st f + E 2 − st f s e 2 e t f s

A c t u a l C o mp e n s a t i o n ( T r a d e o f ) ● S a w mo d u l a t i o n i s i d e a l , b u t i t r e q u i r e s a h i g h p e a k p o w e r . ● S t e p mo d u l a t i o n i s a r e p l a c e me n t , b u t i t h a s a n i mp e r f e c t i o n ( e n e r g y s p r e a d ) . ● I f t < < t , a n o p t i mi z a t i o n f o r P g i v e s s ma l l e r e n e r g y p f 0 s p r e a d .

2 m L - b a n d T W s t r u c t u r e ( P o s i t r o n B o o s t e r ) ● 2 m L - b a n d ( 1 2 9 8 MH z ) d e s i g n e d f o r K E K B i n j e c t o r . ● S a w mo d u l a t i o n : 2 2 . 5 MW i n p u t w i t h 0 . 7 8 A B L g i v e s 1 4 . 4 1 MV / t u b e ( 2 m) ● T h e e n e r g y s p r e a d i s z e r o ( i d e a l ) , b u t t h e v o l t a g e i s v e r y l i mi t e d . 22.5 MW

S t e p Mo d u l a t i o n 22.5 MW ● S t e p mo d u l a t i o n : 1 9 . 5 4 ± 0 . 5 1 MV . ● I f P i s o p t i mi z e d ( l o w e r e d ) f o r l o w e r 0 e n e r g y s p r e a d , 1 7 . 3 8 ± 0 . 1 7 MV . ● T h e g r a d i e n t d e p e n d s o n a c c e p t a b l e e n e r g y s p r e a d a n d w e t o o k 1 7 . 3 8 MV a s o u r w o r k i n g a s s u mp t i o n . 1 9 . 5 4 ± 0 . 5 1 MV . 1 7 . 3 8 ± 0 . 1 7 MV

S - b a n d T W a c c e l e r a t o r ( P o s i t r o n B o o s t e r ) ● 2 m S - b a n d ( 2 8 5 6 MH z ) a c c e l e r a t o r d e s i g n e d f o r K E K B i n j e c t o r . ● S a w mo d u l a t i o n : 2 2 . 5 MW i n p u t w i t h 0 . 7 8 A B L g i v e s 2 3 . 0 3 MV / t u b e ( 2 m) ● S t e p mo d u l a t i o n g i v e s 2 9 . 4 2 ± 0 . 6 9 MV . 36 MW

36 MW O p t i mi z a t i o n Step modulation gives 29.42 ± 0.69 MV. ● P0 optimization does not work, because tf~tp. ● Instead, semi-Step-saw modulation was made ● with the peak power which is less than that for the perfect compensation. The accelerator voltage is determined ● by the acceptable energy spread. 25.49 ± 0.23 MV.