1. Key Physics Topics for Plasma Wakefield Accelerator Research
Topics for Plasma Wakefield R&D at FACET and Beyond
It is a great pleasure and honor to open the 2005 meeting of the APS DPP with a talk on Plasma Accelerators.
There has been remarkable progress made in the past 1-2 years by several groups around the world, and I am delighted to be able to share some of the exciting results with you.
The movie you have been enjoying in the background of this title is courtesy of Frank Tsung . It is a simulation of a laser WFA and you can see a beam emerging from the plasma in this image of plasma density isocontours.
W.B.Mori
University of California at Los Angeles
Much is based on QuickPIC and OSIRIS Simulations
Doe FACET Review February 19, 2008

2. Key Physics follows from energy gain and beam quality considerations
Energy Gain=eEloaded x Lacc
eEloaded= Gradient of Loaded wake
Wakefield amplitude (accelerating and focusing fields)
Beam loading
Lacc= acceleration length
Ldephasing Not an issue for PWFA
Lpumpdepletion High Transformer Ratios
Ldiffraction Head Erosion
Linstability Hosing
Uncompensated Nonlinear
Focusing forces leads to
Emittance growth after several
betatron periods
(effective area increased) x px sx
Plasma focusing causes beam to rotate in phase space
Radially dependent accelerating field leads to energy spread
But by far the most demanding requirements on accels are for HEP
HE -- at least 125 GeV on 125 GeV to discover the Higgs

3. Wake excitation Narrow beams

4. Blowout or Bubble regime for PWFA
Rosenzweig et al. 1990, Lu et al. 2006
Trajectory crossing
Ion channel formed by trajectory crossing
Ideal linear focusing force
Uniform acceleration
Fluid model breaks down!
2D/3D and electromagnetic in nature!
Driven by an electron beam
What do we want to know and predict?
Wake excitation for given drive beam ……
Evolution of drive beam, e.g, instabilities…
Transformer ratio, shaped bunches, train of bunches
Beam loading, beam quality ……
How to put these all together in a design?
What about positrons?
Driven by a laser pulse

5. Wakefields are completely characterized by the trajectory of the blowout radius
W. Lu et al., Phys. Rev. Lett. 16, (2006)
The trajectory of the inner most particle is
Space charge of beam
Ponderomotive force
of laser
Two distinct limits:
Ultra-relativistic blowout
(behind the driver)
Non-relativistic blowout
Nearly a circle!

6. Uniform accelerating field
Field structure in blowout regime
Relativistic blowout regime for blowout radius
Lu et al.PRL 16, [2006]
Bubble radius :
Uniform accelerating field
Linear focusing field

7. Beam Loading linear regime
In the linear regime one superimposes the wake by trailer to the wake by the driver to find the total wakefield [1].
Bunch shaping for no energy spread: Triangular.
The total charge can be found by requiring that all of the energy in the wake is absorbed.
[1] T. Katsouleas, S. Wilks, P. Chen, J. M. Dawson, J. J. Su - Part. Accel, 1987

8. Original simulation results: 1987
Drive beam (laser or particle beam)
Note that wedge gives nearly constant decelerating field
Properly phased trailing beam of particles: Loads wake
In linear theory just use superposition:
Add wakes =>
(for spot size c/wp)
100% energy extraction (though Vgr=0)
100% energy spread
Katsouleas, Wilks et al., 1987

9. Nonlinear beam loading: Solve equation for Rb(x) M
Nonlinear beam loading: Solve equation for Rb(x) M. Tzoufras, in preparation
These equations are integrated for a trapezoidal () to obtain Ez() and rb(). This allows us to design accelerators with 100% beam-loading efficiency that conserve the energy spread.

10. Nonlinear beam loading M. Tzoufras, to be submitted
Nonlinear beam loading theory has been confirmed in fully nonlinear particle-in-cell simulations
Blue arrow is from ions
Green arrows is from beam
Black arrows is the trajectory

11. 25 GeV Stage No energy spread 25 GeV Driver 25 GeV Trailing beam
he ion motion run has the same parameters as the 25gev run except the initial energy of 250GeV. The run was done with 2048x2048x256 cells, and with 0.01 c/wp resolution in transverse direction and c/wp in the longitudinal direction. 4 particle/cell is used. The max compression is 217 n_p, the second plot in that slides is actually blown up from the first plot.
25 GeV Driver
25 GeV Trailing beam
25 GeV Driver
475 GeV Trailing beam
np=5.661016cm-3
Ndriver = 4.421010, r= 3 m, L = 58 m, Energy = 25 GeV
Ntrailing = 1.71010 , r= 3 m , L = 22 m, Energy = 25 GeV or 475 GeV
Rtrans = -Eacc/Edec = 1

12. Pump depletion: Transformer ratio

13. Can the transformer ratio be increased. W
Can the transformer ratio be increased? W.Lu PhD Dissertation UCLA 2007
Linear theory:
Triangular or wedge shaped bunch + precursor leads to constant E_ and an E+ that
Nonlinear blowout regime:
- Starting from equation of Lu et al., it can be shown that the optimal shape of a single bunch is once again a wedge (but without the need for a precursor
np=21016cm-3
Ndriver = 21010, r= 3 m, L = 390 m
Ntrailing = 0.67109 , r= 1 m, L = 15 m
Edec= mcp/e
Eacc= mcp/e
Rtrans= -Eacc / Edec = 10

14. High transformer ratio used a wedge shaped beam
Blowout regime
flattens wake, reduces energy spread
Beam load Ez
Unloaded wake
Loaded wake
Nload~30% Nmax
1% energy spread

15. Multi-bunch Afterburner
Drivers: 75pC*(1:3:5:7)~1nC
Witness: 0.3/R*1nC~50pC
Transf. Ratio ~ 7
Transformer Efficiency ~ 30%
Themos Kallos, USC

16. Hosing (Head-tail) Instability
Caused by the coupling between the beam and the electron sheath at the ion channel boundary.
Triggered by head-tail offset along the beam and leads to the transverse beam centroid oscillation with a spatial-temporal growth.
Electron hosing and positron transverse instabilities are likely the biggest obstacles for PWFA (or LWFA) to impact HEP applications. It will cause steering errors as well as limit the energy gain, degrade the beam quality and lead to beam breakup.

17. How severe is hosing?
The coupled equations for beam centroid(xb) and channel centroid (xc) (Whittum et. al. 1991):
where
Standard theory predics oscillation and exponential growth
Asymptotic solution
for a linearly tilted beam
kbs= kbLpd=(g/2)1/2/e-

18. Hosing in the blow-out regime
Huang et al., Phys. Rev. Lett. Phys. Rev. Lett. 99, (2007)
Parameters:
Ipeak = 7.7 kA

19. Minimal hosing and emittance growth!
25 GeV stages
Minimal hosing and emittance growth!
25 GeV Driver
25 GeV Trailing beam
25 GeV Driver
475 GeV Trailing beam
np=5.661016cm-3
Ndriver = 4.421010, r= 3 m, L = 58 m, Energy = 25 GeV
Ntrailing = 1.71010 , r= 3 m , L = 22 m, Energy = 25 GeV or 475 GeV
Rtrans = -Eacc/Edec = 1

20. Head erosion Matched propagation of beam body:
For matched beams head erosion is an issue:
Difficult to achieve matched propagation without head erosion for an ordinary beam (i.e., uniform emittance and spotsize).
Possible solutions:
1. External focusing
2. Muliple stages such that L of each stage is shorter
3. Trumpet shaped beams that can be produced using a plasma lense.
4. Emittance growth at the head

21. Beam head erosion in field ionized plasmas

22. Beam head erosion in field ionized plasmas
MM. Zhou, in preparation
Slowed down free expansion
between A & B
(by a factor 0<<1)
Vacuum
expansion
Slower
Ionization
front
Pinch
point
Ion
Focusing

23. Synchrotron radiation
betatron radiation

24. Ion Motion Ion motion when
Matched beam spot size shrinks at large g, low en
For future collider
eny down by 102 (e.g., 10nm-rad)
g up by 10+
nb up by 102
Ion motion must be included in design/models
Could cause emittance growth
Could cause energy spread
Could increase betatron radiation to unacceptable levels
Ref. S. Lee et al., AAC Proc (2000); J. Rosenzweig et al., PRL (2006)

25. Ion Motion Ion motion nb=1.3x1019 nb/n0 m/M=350/1836=.125
np=5.661016cm-3
Ndriver = 4.421010, r= 3 m, L = 58 m, Energy = 250 GeV `nb=1.91x1019
Ntrailing = 1.71010 , r= 3 m , L = 22 m, Energy = 250 GeV nb=1.41x1019
Rtrans = Eloaded/Edec = 1
Ion motion

27. Positron Acceleration 3-D QuickPIC Simulations, plasma e- density
• “Uniform” focusing force (r,z)
• Non-uniform focusing force (r,z)
Smaller accelerating force
Ref. S. Lee et al., Phys. Rev. E (2000); M. Zhou, PhD Thesis (2008)

28. Positron acceleration
Head erosion
5.7GeV in 39cm
Evolution of a positron beam/wakefiled and final energy gain in a field-ionized plasma

29. Positron Acceleration: Needed for e-e+ collider Only at FACET A few scenarios
Positrons are accelerated on a positron wake
Hollow channels might be needed
Use linear wakes
Positrons are accelerated on an electron wake
One idea for injecting positrons onto an electron wake will be discussed in Mark Hogan’s talk
Beam loading by narrow intense positron bunches has not been tackled theoretically as of yet
Ref. S. Lee et al., Phys. Rev. E (2000); M. Zhou, PhD Thesis (2008)

30. Summary Recent success is very promising
experiments
theory
simulation (PIC and reduced PIC)
No known show stoppers to extending plasma accelerators to the energy frontier
Many questions remain to be addressed for realizing a collider
Experiments
Theory
simulation
FACET-class facility is needed to address them
Lower energy beam facilities cannot access critical issues in the regime of interest
FACET can address most issues of one stage of a 5-20 stage e-e+ TeV collider
But by far the most demanding requirements on accels are for HEP
HE -- at least 125 GeV on 125 GeV to discover the Higgs

31. 25 GeV Stage No energy spread 25 GeV Driver 25 GeV Trailing beam
he ion motion run has the same parameters as the 25gev run except the initial energy of 250GeV. The run was done with 2048x2048x256 cells, and with 0.01 c/wp resolution in transverse direction and c/wp in the longitudinal direction. 4 particle/cell is used. The max compression is 217 n_p, the second plot in that slides is actually blown up from the first plot.
25 GeV Driver
25 GeV Trailing beam
25 GeV Driver
475 GeV Trailing beam
np=5.661016cm-3
Ndriver = 4.421010, r= 3 m, L = 58 m, Energy = 25 GeV
Ntrailing = 1.71010 , r= 3 m , L = 22 m, Energy = 25 GeV or 475 GeV
Rtrans = -Eacc/Edec = 1