Ionization Injection E. Öz Max Planck Institute Für Physik

*AWAKE technical design report 2015 Current AWAKE Injection Scheme Is there any other way?

E.Oz No analytical expression exists for 3 D relativistic wave breaking (Particle trapping) Maximum Amplitude of a Plasma Wave: WAVE BREAKING (Particle Trapping) in History

E.Oz Akhiezer and Polovin, 1956 : 1-D relativistic cold WB Not consistent with SLAC results! J. M. Dawson, 1959 : 1-D non-relativistic cold WB Neighboring sheets cross, i.e. wave breaks and plasma electrons are self trapped 1-D Theory of WAVE BREAKING (Particle Trapping) in History

E.Oz The wake grows from and instability, therefore the onset of trapping is not controllable Self Modulated Laser Wake Field Accelerator Laser Self Trapped Plasma Electrons Injection Mechanism for Laser Wake Field Experiments (LWFA): Trapping A peak field of 100 GV/m is enough to cause WB and self-trapping and consistent with the 1D theory What is the physics of trapping in SLAC PWFA?

Li+ He+ Bunch does not ionize He I ( eV), but does ionize Li I (5.392 eV) Bunch is focused by the wake in the Li I plasma Bunch ionizes He I ( eV), but not Li II (75 eV) Li (Particle Trapping) at SLAC PWFA

OSIRIS Simulation: Real Space (r-z) Of Li & He Electrons Li at z=11.3 cm He at z=22 cm He at z=11.3 cm Lithium electrons support the wake He electrons trapped inside the wake He electrons reach 2.5 GeV 2-3  m long Ultra Short bunches What is the difference between a He electron and a Li electron?

e - : Pre-ionized (Li) e - : Ionized inside the wake (He) -v    Longitudinal Wake Amplitude 3-D Potential  v   z v  : Plasma Wake Phase Velocity -v  T RAPPING IN I ONIZING W AKE Just like marbles rolling over a hill, It’s easier to turn the marble starting at the bottom around The difference is the ionization potential! (He 24.6 eV vs. Li 5.4 eV)

E.Oz Constant of motion for arbitrary wave potentials of the form, A= A(z-v  t),  =  (z-v  t) Analytical Model of Trapping Condition for trapping maximum of the potential For particles born near axis vv v Trapping condition for the potential How about AWAKE?

E.Oz What is 1-d relativistic the wavebreaking limit for AWAKE?

p Trapping Threshold For AWAKE

Can it be done at AWAKE? Path to AWAKE: Evolution of the concept A. Caldwell et. Al.

External Injection Ionization Injection Method 1 Method 2 laser1 laser2 Extenal e - beam internal e - beam Plasma species 1 Plasma species 2 Plasma species 1 Plasma species 2 Plasma species 1 internal e - beam What is the idea?

Methods Ionize a gas mix Ionize gas puff (e.g Hydrogen 13.5 eV ) Ionize second electron of Rb (27.28 eV) Laser intensity scales as 4 th power of ionization potential (13.6/4.18)^4 ~110*I Rb I rb =1.7 x10 12 W/cm 2 (27.28/4.18)^4 ~1800*I Rb This type of injection will avoids initial density ramps The location of injection along plasma source can be quite flexible.

Osiris Simulation

Some of the properties of ionization injected electrons Trapping condition and short ionization region Imposesbunch length will be a fraction of the plasma Wavelength,  << p They are ionized with a small radial Momentum plus the trapping condition makes them potentially low emittance Number of injected electrons limited by available second species and beam loading should be comparable to external injection If trapped particles are collected continuously the will be large energy spread since the particle At same  position experience same wakefield but if they are picked up at different time they will have drastically different energies in order to reduce energy spread the trapping region must be limited by limiting the second gas species location or By only ionizing in a narrow location, crossing laser

Conclusions External injection for AWAKE is challenging An alternative could be ionization injection (IE) IE avoids initial density ramps For IE location of injection along plasma source is quite flexible. Accelerating fields of ~ 1 GV/m can trap electrons ionized inside the wakefield Trapped electrons can have high charge, low emittance, short bunch length Trapped electrons can be regarded as probes for the wakefield amplitude and period (multiple bunches)