1. PWFA Experiments in Static Fill Argon Some numbers issues and mysteries Ken Marsh 5/30/2013

2. M1. How did we get 20-30 GeV gain when we should be very limited by head erosion? Li = 5.4 eV, Ar = 15.8 eV, relative reduction in HE length (15.8/5.4) 1.73 = 6.4 L HE ≅ σ z /v etch Comparing Li to Ar ionization potentials 20 GeV in 12 cm is 170 GeV per meter!

3. 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 σ r was larger than 20 um How was full Ionization achieved?

4. Some basic parameters for 20 Torr Argon Density Range 10% ionized 7x10 16 100 % ionized 7x10 17 cm -3 Normalized beam parameters For σ r = 10 μm, k p σ r =.5 to 1.5 For σ z = 20 μm, k p σ z = 1 to 3

5. 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 ≥ 1.6σ r Blow out radius/ionization radius ≅ R b /1.6k p σ r ranges from 3.75 to 1.25 Thus favoring higher density plasma! Normalized blow out radius

6. 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 n e = 4x10 17 cm -3 β =.2 cm. The FACET betas were 10 cm and 100 cm. Betatron motion and X-ray generation hν c = 32 MeV Power radiated ~ n 2 r 2 Divergence k b r Total counts on Lanex ~r 2

7. 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?

8. M6. Smelled like sulfur after opening vacuum Photo spallation argon? Arhν S α

9. 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 > R blow How is full Argon ionization achieved? And some ionization of Helium?

10. Why you should not do PWFA experiments with bounded gas volume