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

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

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

Plasma wiggler – Undulator from betatron motion A. Rousse et al., Phys. Rev. Lett. 93, 135005 (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. 93 135004 (2004)

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

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

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).

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

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.

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.

Thank you for your time Questions?