1. Wakefield issues due to a slotted foil for a THz source
Juergen Pfingstner
11 August 2017

2. Content
THz source for SwissFEL
Foil wakefields
Summary

3. 1. THz source for SwissFEL

4. THz source for sample excitation at SwissFEL
Motivation:
High demand from material scientists for THz source.
Pumb probe experiments.
Challenging specifications:
State of the art of THz sources:
Very small bandwidth but low power.
High power, but broadband radiation.
The needed intermediate regime is not really covered:
Narrow-bandwidth (< 10%).
Wide-range tunable ( THz).
Pulse-energy > 100 μJ.
Fixed phase from pulse to pulse.
Studied solution:
Electron beam in undulator which is tuned to correct frequency: free-electron laser.
Prebunching to ensure fixed phase relation.
Bunching tunable from 1 to 5 THz. Then tune undulator on higher harmonics.
Problem: creation of the pre-bunched beam.

5. Slotted-foil technique with transverse deflecting cavities (TDC)Ut
Beam is not stopped by foil, but spoiled.
Beam energy is 27 MeV. s
foil Ut Δx
LD = 1.5m
Transverse deflection cavity
Alias crab cavity
X-band linear enough for 3mm beam length
For 10% BW≈1/Nb, 10 micro-bunches are necessary.
1 THz: λ = 300μm (66μm at 4 THz)
Min. bunch length: 3mm.

6. Bunching at 1 THz Bunching at undulator
No smearing due to beam transport visible in spectrum.
But not much higher order frequency content.

7. Bunching at 4 THz Bunching at undulator.
At the moment beam is cut by foil, to avoid to large aperture and dispersive effects.
Some smearing due to beam transport from foil to undulator.
Problem: Apparently hardly any higher order frequency content.

8. 2. Foil wakefields

9. Estimates for wakefields from foil 1/2
Only reference found: K. Bane and G. Stupakov , PRSTAB 7, (2004):
“Transition Radiation Wakefield for a Beam Passing through a Metallic Foil.”
Assumptions:
Gaussian beams.
Only foil, no slits.
Three different estimates
Pencil beam (Gaussian): σZ >> σx
Large beam (bi-Gaussian): : σZ << σx
Could be a good approx. because beam length = 3mm and Δx = 3cm.
Tilted beam (tri-Gaussian):
Most accurate
But many approximations in calc.

10. Estimates for wakefields from foil 2/2
Longitudinal wakefield:
Pencil beam estimate: Δδmax = 0.43%.
Tilted beam (on-axis particles): Δδ = 0.56%
This energy change can most likely be neglected.
Transversal wakefield:
Estimates for Pencil and large beam, give a varying relative kick of about 0.5.
Most realistic estimate for tilted beam gives a value only for the centre of the beam : Δxp/σxp = -1.9.
Significant effect: detailed EM-field simulations necessary!

11. Physical picture (Chao)
Charge passing through two plates
Charge passing through one plate
beam
Not familiar with surface charges and eddy currents of relativistic particles:
Initial Coulomb field is reflected at the foil.
Charge -q is traveling with speed of light outward. Why?
If there is a strongly tilted beam, are there some particle missing the radiation ring?

12. Effect of slits . . . foil Transition radiation from beam through foil
Diffraction radiation from beam through foil . . .
Model beam as beam sliced through foil and slits.
Overall wakefield is a mixture of both radiation effects.
Detailed EM simulations would be helpful.

13. 3. Summary
Design of a THz radiation source based on transverse deflecting cavities is considered.
Overall facility length of 10m.
Transverse wakefield issue:
Wakefields from slotted foil could still be a problem for beam transport.
Urge to include especially the transverse wakefields.
Estimates from Bane/Stupakov paper, but deviation from the THz source case:
No slits in foils.
Non-Gaussian beam distribution.
Different estimates for trans. wakefields give up to a factor 4 different values.
No good understanding from my side for the physical happening behind formulas.
Detailed EM simulations would be very valuable.