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PWFA Experiments in Static Fill Argon. Some numbers issues and mysteries. Ken Marsh 5/30/2013. M1. How did we get 20-30 GeV gain when we should be very limited by head erosion?. L HE ≅ σ z /v etch. Comparing Li to Ar ionization potentials. Li = 5.4 eV , Ar = 15.8 eV ,
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PWFA Experiments in Static Fill Argon Some numbers issues and mysteries Ken Marsh 5/30/2013
M1. How did we get 20-30 GeV gain when we should be very limited by head erosion? LHE ≅ σz /vetch Comparing Li to Ar ionization potentials Li = 5.4 eV,Ar = 15.8 eV, relative reduction in HE length (15.8/5.4)1.73 = 6.4 20 GeV in 12 cm is 170 GeV per meter!
M2. Sub 10 um beam size required to tunnel-ionize argon,but For typical beam parameters β and ε, Calculated beam size σ = (βε)1/2 = 10 to 20 um Measured σr was larger than 20 um How was full Ionization achieved?
Some basic parametersfor 20 Torr Argon Density Range 10% ionized 7x1016 100 % ionized 7x1017cm-3 Normalized beam parameters For σr = 10 μm, kpσr = .5 to 1.5 For σz = 20 μm, kpσz = 1 to 3
M3. Expected blow out radius is greater than the ionization radius Based on the maximum radial electric field of the e-beam, the estimated tunnel ionization radius is ≥ 1.6σr Normalized blow out radius Blow out radius/ionization radius ≅ Rb/1.6kpσr ranges from 3.75 to 1.25 Thus favoring higher density plasma!
M4. Beam Mismatch Assuming no density ramp up to reduce the beam size and improve the match, there is a severe mismatch, especially at higher plasma density. For ne = 4x1017 cm-3β = .2 cm. The FACET betas were 10 cm and 100 cm. Betatron motion and X-ray generation hνc = 32 MeV Power radiated ~ n2r2 Divergence kbr Total counts on Lanex ~r2
M5. Helium Ionization and Trapping • Ionization was observed in pure helium • IP Helium 24.6 eV, IP Argon 15.8 and 27.6 eV • Is ionization trapping from ArII possible? ArIII?
M6. Smelled like sulfur after opening vacuum • Photo spallation argon? S hν Ar α
Summary Unexpected Results • High Energy gain despite limits by HE • Results, in theory, favor high density plasma formation • Without density ramp, beam is severely mismatched. Consider time like density ramp. • In all cases, results favor full ionization with radius of ionization > Rblow • How is full Argon ionization achieved? • And some ionization of Helium?
Why you should not do PWFA experiments with bounded gas volume