Download Considerations of the proton bunch compression for PDPWFA

Considerations of the proton
bunch compression for PDPWFA
G. Xia and A. Caldwell
Dec 9, 2008
Outline
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Proton driven plasma wakefield acceleration
Short proton bunch production
Preliminary design of bunch compressor
Conclusions and outlook
Proton bunch driven PWFA
•  Our new idea is to use existing high energy
proton bunch to drive high enough electric field
to accelerate the electron beam to high energy *.
•  Ultimate goal is to construct an e+e- collider at
energy frontier, the cms energy is beyond TeV.
•  Particle in cell simulation give very promising
results.
•  Therefore actions are needed to further study on
this issue.
* See A. Caldwell et al., arXiv: 0807.4599.
Proton bunch driven PWFA
•  Pros and cons of using proton bunch
•  Pros: already exiting high energy > 1 TeV;
high bunch intensity, more than 1011.
•  Cons: not easy to get short bunch (Hsource+convertor target = long proton
bunch)
•  Although novel idea exists to use laser
beam to get low emittance and short
proton bunch in recent years
Short bunch production
•  There are various ways to realize the short bunch, most
commonly used are velocity bunching and magnetic
compression.
•  Velocity bunching uses RF field to modulate the energy
within a bunch and then the bunch drifts a certain
distance and gets short.
•  Magnetic compression firstly needs enough positionenergy correlation from RF section, and then the beam
goes through a dispersive path and the head and tail of
the bunch converge to each other and shorten the bunch
length.
•  Some other novel ideas to get short proton bunch such
as beam cooling in 6D phase space, laser striking of thin
foils, etc.
Velocity bunching
•  Bunch compression is performed by velocity modulation
within a bunch
•  In general, bunch head is decelerated and beam tail is
accelerated
•  Velocity is modulated according to
•  Therefore, velocity modulation is saturated to c at γ>>1. It
works only for low energy particles (after injectors)
Magnetic compression
•  Position-energy correlation scheme: the bunch rides on zerocrossing RF field and get the highest correlation between position
and energy.
•  This correlation can be realized by conventional RF sections or by
plasma wakefield.
•  The first scheme is investigated in detail.
magnetic compressors
Chicane
Double chicane
Chicanes as a Wiggler
Arc as a FODO-compressor
Which one is better for our case?
Energy chirp
•  Using plasma wakefield and conventional RF field to
introduce the position-energy correlation
e- beam injection
High energy ebeam for lepton
collider
Plasma channel
for beam chirp
Magnetic chicane for
bunch compression
Plasma channel
for acceleration
e- beam injection
High energy e- beam
for lepton collider
Conventional RF
section for beam
chirp
Magnetic chicane for
bunch compression
Plasma channel for
acceleration
Energy chirp by plasma wakefield
•  If we consider using plasma wakefield for energy chirp, the bunch
length should be the same order as the plasma wavelength
•  Plasma wavelength is as following
here, n0 denotes the plasma density, me
the mass of electron, ε0 the permittivity of
vacuum, c the speed of light
•  If we use bunch length 10 cm, the corresponding plasma density is
1.12e17 m-3, namely, 1.12e11 cm-3.
•  Since the acceleration gradient is proportional to the square root of
plasma density, scaling with SLAC energy doubling experiment (50 GV/
m, 2.7e17 cm-3), the acceleration gradient is about 32 MV/m.
•  It seems that this scenario has no advantage compared to the
conventional RF system.
Magnetic chicane
•  Magnetic compression principle
Principle of magnetic compression
•  Beam transport matrix
•  Without coupling
Principle of magnetic compression
•  Drift space
•  Dispersive area
•  Energy modulation
Principle of magnetic compression
•  If the beam is zero-crossing
•  The total matrix for magnetic compression
•  Therefore, if
is satisfied, the bunch
length is minimum.
•  The final bunch length is
High energy colliders
4-bending magnet chicane
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For the 4 identical dipole case, R56 can be expressed by
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We will consider using LHC main dipole peak field, say, 8.3 Tesla. In order to
bend 1 TeV proton beam, the required bending radius is
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Then we still use 14.3 m as the length of LHC dipole, the bending angle of
dipole is
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L=14.3 m, bending angle is: 0.0355828 rad, the length of dipole is 14.3 m; the
drift distance between the two dipoles is around 385 m. The total length for
bunch compression section (RF + magnetic chicane is about 3.5 km)
Magnetic compression
•  From the linear theory of magnetic compression, we can
work out a set of parameters which can realize the short
proton bunch production.
•  Using 2.7 km superconducting cavities to produce the
energy chirp within the bunch and then make the beam
pass through 830 m long magnetic chicane and then we
can get short proton bunch.
ΔΕ/Ε
ΔΕ/Ε
Z
ΔΕ/Ε
Z
RF
ΔΕ/Ε
Z
Dispersive Section
ΔΕ/Ε
Z
Z
Chicane parameters
Parameter
Symbol
Value
Bunch charge
N
1011
proton energy
E0
1
TeV
(dE/E)i
0.01
%
Bunch length before BC (FWHM)
Δzi
10
cm
Bunch length after BC (FWHM)
Δzf
100
µm
Initial relative energy deviation
Compression ratio
Unit
~1000
Momentum compaction (MC)
R56
-1.0
m
Second order of MC
T566
1.50
m
Bend angle per dipole
θ
0.03558
radian
Bend magnet length
LB
14.3
m
Drift from bend–1 to 2 (to put collimators, diagnostics, beam dump etc.)
△L
385
m
Drift from bend–2 to 3 (put quads as well to preserve the beam quality)
△Lc
2.8
m
Total BC length (projected)
Ltotal
830
m
Magnetic field strength
B
8.3
Tesla
Bending radius
ρ
401.8795
m
(dE/E)f
10
%
Final energy spread
Similar to the LHC beam parameters.
Requirements of the RF
•  We use the SPL RF parameters. Vacc=25
MV/m, Lcav=1.837 m ?, Freq=704 MHz.
•  Proton bunch rides on the zero crossing of
RF phase to get a high enough positionenergy correlation.
•  Length of RF section is about 2.7 km.
•  Total length of bunch compression is
about 3.5 km which includes the RF,
quadrupoles and chicane.
Simulation of short proton bunch
•  MatLab to produce 6D
particle distribution, e.g.
1000 particles.
•  The particles go through
the RF plus magnetic
compression sections
(MAD defined beam line),
(RF+Chicane), record
each particle‘s final
coordinates.
•  Analyze the particle
coordinates and see
whether they get
compression in length.
Initial beam parameters
Parameters
Symbol
Value
Units
Proton bunch intensity
Np
1011
Beam energy
Ep
1
TeV
Initial bunch length, RMS
σz
10
cm
Initial momentum spread
Δp/p
1.0e-4
Horizontal emittance
εx
1.2e-8
m·rad
Vertical emittance
εy
1.2e-8
m·rad
6D Gaussian distribution
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x=randn(1000,1)*1.6E-5;
px=randn(1000,1)*3.1E-5;
y=randn(1000,1)*1.6E-5;
py=randn(1000,1)*3.1E-5;
z=randn(1000,1)*0.1;
delta=randn(1000,1)*1.E-4;
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fid=fopen('ggg1.txt','w');
for m=1:length(x)
fprintf(fid,'start,x=%12.6g,px=%12.6g,y=%12.6g,py=%12.6g, &
\n',x(m),px(m),y(m),py(m));
fprintf(fid,'
t=%12.6g,delta=%12.6g\n',z(m),delta(m));
end
fclose(fid);
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TESLA bunch compression
TESLA bunch compression
Before BC
After BC
Longitudinal phase space distortion due to nonlinear of RF
field, can be cured by 3 rd harmonic RF system
Longitudinal phase space
Bunch length of 1 cm and energy spread of 10-3
Bunch length of 10 cm and energy spread of 10-4
Gaussian distribution of intial beam
BEND1: SBEND,L=14.3,ANGLE=0.03558, E1=0.0,E2=0.03558
BEND2: SBEND,L=14.3,ANGLE=-0.03558,E1=-0.03558,E2=0.0
BEND3: SBEND,L=14.3,ANGLE=-0.03558,E1=0.0,E2=-0.03558
BEND4: SBEND,L=14.3,ANGLE=0.03558, E1=0.03558,E2=0.0
D1: DRIFT, L=385.0
D2: DRIFT, L=2.8
D3: DRIFT, L=385.0
QF: QUADRUPOLE, L=0.5, K1=0.01
QFH: QUADRUPOLE, L=0.25, K1=0.01
QD: QUADRUPOLE, L=0.5, K1=-0.01
! define the beam line
BC: LINE=(BEND1,D1,BEND2,D2,BEND3,D3,BEND4)
BCRF1: LINE=(35*CAV,QF,35*CAV,QD)
BCRF: LINE=(21*BCRF1, BC)
! define the beam parameters.
E0:=1000.0
BEAM, PARTICLE=PROTON, ENERGY=E0, EX=1.2e-8, EY=1.2e-8, SIGT=1e-1, &
SIGE=1.0e-4, NPART=1e11, RADIATE=.FALSE.
! Cavity definition
RF_ON := 1
CAV : LCAV, FREQ = 704, L = 1.837, VOLT=25.0, DELTAE = 46.0, &
PHI0 = 0.0, ELOSS = 1.4e+13
USE, BCRF
SELECT, OPTICS, CLEAR
SELECT, OPTICS, #S/#E
OPTICS, COLUMNS= NAME, S, L,
&
BETX, ALFX, MUX, DX, DPX, &
BETY, ALFY, MUY,
&
K0L, E1, E2, K1L, K2L &
FILENAME= "BCRF_Lat1.txt"
USE, BCRF
PRINT, #E
TWISS, SAVE
PLOT, TABLE=TWISS, HAXIS=S, VAXIS1=BETX,BETY, VAXIS2=DX, &
STYLE=1, COLOUR=100, SPLINE=.T., FILE="BC2.txt"
BEAM, PARTICLE=PROTON, ENERGY=E0, NPART=1.0E11
EMIT
! Start a new track
USE, BCRF
BEAM, PARTICLE=PROTON, EX=1.2E-8, EY=1.2E-8,ET=1.0E-5, ENERGY=1000.0
TRACK
call, 'ggg1.txt'
RUN, TURNS=1, FPRINT=1
PLOT, HAXIS=X, VAXIS=PX, MULTIPLE
PLOT, HAXIS=Y, VAXIS=PY, MULTIPLE
PLOT, HAXIS=T, VAXIS=ET, MULTIPLE
ENDTRACK
STOP
Optical functions of BC
Conclusions and outlook
•  Short proton bunch can be realized by conventional
magnetic compression, which is confirmed from linear
theory.
•  Simulations of short proton bunch is still ongoing.
•  Open questions remain, how to design a cheaper bunch
compression system? Is one stage magnetic
compression enough for our 1000X compression? Beam
dynamics issues in the compression? etc
•  The aim is to design a self-consistent PDPWFA based e
+e- collider.
•  Concerning the luminosity of collider, we will further work
on the small beam sizes, low emittance preservation,
and good repetition rate.
Acknowledgement
Thanks for the illuminating discussions
with Toshi Tajima, Frank Zimmermann,
Andy Wolski, Rainer Wanzenberg, Weiren
Chou, et al.