1. Betatron radiation sources
Nathan Majernik
October 15, 2015
FACET-II Science Opportunities Workshop

2. Oscillatory motion gives synchrotron radiation
Undulator Radiation
Oscillatory motion gives synchrotron radiation
K, first harmonic, wiggler vs undulator, tech limitations
P. Schmuser. Free-Electron Lasers in the Ultraviolet and X-Ray Regime
Typical value: ~1 (LCLS 3.5)
Typical value: ~10 keV

3. SPring-8 10T wiggler
Design, right chart, left chart, significance

4. Plasma wiggler – Undulator from betatron motion
A. Rousse et al., Phys. Rev. Lett. 93, (2004).
Typical value: ~100
(Requires large offset, x0kp ~1)
Typical value: ~100 keV
1T vs 10^17-10^19 plasma = 300 MV/m, K calc+example, cutoff experiment+SLAC class theory
Plasma wigglers can give magnet field equivalents of >100T with <cm wavelength
How to excite and control amplitude?
S. Kiselev, et al., Phys. Rev. Lett (2004)

5. Resonant betatron excitation
Short undulator resonantly excites betatron amplitude
Idea presented to SLAC SAREC
Undulator, plasma wiggler, resonance, PIC, first order results

6. Light output
Bottom plot, undulator=blue RBE=red, deviation from sine, FFT. Who cares? Adiabatic and stability.

7. E166 – Polarized Positrons
FFTB ~50 GeV beam
Production of 80% polarized positrons
“Polarized positrons can be produced via the pair-production process initiated by circularly polarized photons … higher intensity beams … than decays from radioactive nuclei”
“The value of K in the present experiment was small, about 0.17, because of practical limitations to the current in the (pulsed) undulator.”
Polarization, signal rate + background process, probe new particle properties, constrain SUSY. Traditional source. E166: photons -> positrons, 80%. Design. FFTB = 8 MeV. K limitation. No plasma wiggler like planar
G. Alexander et al., Nucl. Instrum. Meth. A610, 451 (2009).

8. Unique opportunity for helical betatron undulator
RBE. No need for big B. Litos. Sum up.
Pair helical undulator with PWFA over ~meter length scales.
Recent results from Litos at FACET are encouraging, showing formation of >1m preformed plasma channels with 10TW laser and axicon lenses.
Experimental outlook: Possibility for E210 experiment. Highly promising for FACET-II

9. Ion channel laser (ICL)
Magnetic wiggler:FEL::Plasma wiggler:ICL
SASE to bunch beam for coherent radiation
Appeal: Potential for extremely compact devices
“ρ can attain values as high as 0.03” (Ersfeld, 2014)
Problem: Original theory (Whittum, 1990) has imposed constraints on beam quality and amplitude that made ICLs impractical for >IR radiation
“It should be emphasized, however, that such an x-ray laser could not be realized without a sharp distribution in transverse energy, corresponding to a step radial profile”
Problem = constraint -> 100m undulators.

10. Both problem and solution?
Unlike a magnetic undulator, which externally sets periodicity, ICL oscillation frequency depends on betatron amplitude
This point was neglected in plasma wiggler discussion
Recent work (Ersfeld, 2014) has explicitly considered this second order effect and shown that the ICL equations can be expressed as FEL (with SC) equations
In doing so, the constraints on the beam specifications and oscillation amplitude were loosened
Gives example for a UV, 200 nm, ICL: Requires 150MeV, εn~4E-8 πm, np~2E16 cm-3, I~600A, lg=4.5cm, 2GW output
Combine with RBE?
Although the external magnetic fields are much weaker than the internal fields, their resonant nature means significant impact may be possible
Greater control with less dependence on initial conditions
Helical case much easier
Contrast with Whittum.

11. Thank you for your time Questions?