1. Parameter sensitivity tests for the baseline variant Konstantin Lotov, Vladimir Minakov, Alexander Sosedkin Budker Institute of Nuclear Physics SB RAS, Novosibirsk, Russia Novosibirsk State University, Novosibirsk, Russia AWAKE Collaboration

2. presented by K.Lotov at AWAKE collaboration meeting, Geneva 05.12.2013 The baseline variant: Infinite plasma Half-cut beam discussed here discussed earlier no study or interest

3. presented by K.Lotov at AWAKE collaboration meeting, Geneva 05.12.2013 Variations of plasma density: It is convenient to characterize the field by the noise-resistant wakefield potential  and use  max (z) as the integral measure of wakefield quality  max 2e14 3e14 5e14 7e14 1e15 1.5e15 2e15 3e15 5e15 High density plasmas support stronger fields, but hosing or filamentation may develop The baseline is at the optimum excitation efficiency 2e14 3e14 5e147e141e15 1.5e15 2e153e15 5e15 n 0 *50/7, E 0 *7,  E = const,  : 0.1 -> 3/16, E m /E 0 : 0.37 -> 0.22 limit due to elongation of wave period: not enough bunches to reach saturation field

4. presented by K.Lotov at AWAKE collaboration meeting, Geneva 05.12.2013 Variations of ion mass: 1 (H) 6.9 (Li) 24.3 (Mg) 85.5 (Rb) 39.9 (K) 7794133 (Cs)197 (Au) Rubidium is heavy enough to have no problems with ion motion

5. presented by K.Lotov at AWAKE collaboration meeting, Geneva 05.12.2013 Variations of driver population: 5e11 4e11 3.5e11 3e11 2.5e11 2e11 1.5e11 1.15e11 The baseline regime is close to the limit (~40% of wavebreaking field), further increase of population does not result in proportional field growth N 1/3 The limit due to nonlinear elongation of the wakefield period: K.V.Lotov, Phys. Plasmas 20, 083119 (2013)

6. presented by K.Lotov at AWAKE collaboration meeting, Geneva 05.12.2013 Variations of driver length and population (constant peak current): 8 cm 6 cm 12 cm 20 cm Fewer bunches at shorter lengths produce proportionally weaker fields, but more bunches make no sense, as the limit is reached

7. presented by K.Lotov at AWAKE collaboration meeting, Geneva 05.12.2013 Variations of driver length (constant population):  z =6 cm  z =12 cm  z =24 cm Weak dependence, fewer and denser macro- bunches are more efficient In the linear model, the field is determined by the total driver charge and independent on how many bunches it is distributed over.

8. presented by K.Lotov at AWAKE collaboration meeting, Geneva 05.12.2013 Variations of driver radius (constant emittance): 0.2 mm 0.25 mm 0.3 mm 0.5 mm 0.15 mm 0.1 mm 0.05 mm Wide beams are not dense enough to drive the wave to the limiting field Narrow beams are quickly diverging due to the transverse emittance Baseline radius is the optimum one for this emittance Beam fragments at z=3.6 m: r b =0.2 mm r b =0.05 mm

9. presented by K.Lotov at AWAKE collaboration meeting, Geneva 05.12.2013 Variations of the driver energy: 100 200 400 600 800 10002000 GeV /W b 1/2 Weak dependence: peak field is near saturation, W b 1/2 scaling of the length (at constant normalized emittance)

10. presented by K.Lotov at AWAKE collaboration meeting, Geneva 05.12.2013 Variations of driver energy spread: 0.17% 0.35% 0.7% No dependence

11. presented by K.Lotov at AWAKE collaboration meeting, Geneva 05.12.2013 Variations of driver emittance (angular spread): 1e-5 2e-5 3e-5 4.5e-5 4e-5 5e-5 7e-5 1e-4 2e-4 Lower emittance: same fields, slower beam destruction Higher emittance: lower fields

12. presented by K.Lotov at AWAKE collaboration meeting, Geneva 05.12.2013 Variations of cut location: propagation length fraction remained 20% 25% 35% 50% 65% 95% 80% Late cut: no beam to excite high fields Early cut: slow instability growth, beam has time to diverge Optimum:  z ahead of the center 01224-12-24 cm from the center

13. presented by K.Lotov at AWAKE collaboration meeting, Geneva 05.12.2013 Varying plasma radius: E.Oz, P.Muggli, NIMA paper: simulations cone-shaped plasma infinite plasma (baseline) fears: detuning of the wave frequency, different wave structure, different trapping conditions no more Wakefield phase: regions of stable phase velocity are still there has small effect on wakefields Wakefield amplitude: changes are small

14. presented by K.Lotov at AWAKE collaboration meeting, Geneva 05.12.2013 Summary: Infinite plasma Cut location Sensitivity, S  max /  max = S  X/X 0.7 0 (extremum) 0.4 0 0.3 0.07 0 0.3 0 1 50% The way to higher fields: lower emittance, smaller beam radius, higher plasma density Of less importance: increase of beam peak current False target: increase of beam population at the expense of elongation

15. Thank you