1. Wakefield excitation by the train of equidistant bunches Konstantin Lotov 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, Duesseldorf 21.06.2013 Simulations: there is a field limit which is difficult to overcome It is more convenient to characterize the field by the noise-resistant wakefield potential: 1 – Baseline AWAKE variant 2 – Like baseline, but negatively charged driver 3 – Like baseline, but 10 times lower driver emittance 4 – Like baseline, but 4 times shorter driver and 16 times higher plasma density 5 – Like baseline, but 4 times shorter driver 40% of wavebreaking field

3. presented by K.Lotov at AWAKE collaboration meeting, Duesseldorf 21.06.2013 Why the field saturates? Reality: complicated picture (btw, seen why  is better) Simplified model: train of rigid equidistant bunches, the peak current is the same, as is the maximum field. Reason: wakefield and bunches are out of phase (btw, the field growth is almost linear)

4. presented by K.Lotov at AWAKE collaboration meeting, Duesseldorf 21.06.2013 Why the wakefield period is not 2  c/  p ? Possible reasons: plasma current driven wave wave nonlinearity Changing the driver current: 1: very wide single p + bunch (  r =15 c/  p ) 2: wide single p + bunch (  r =3 c/  p ) 3: single p + bunch (  r =c/  p ) 4: 5 normal p + bunches (  r =c/  p ) 5: 5 normal p - bunches (  r =c/  p ) 6: 5 narrow p + bunches (  r =0.3 c/  p ) 7: 5 narrow p - bunches (  r =0.3 c/  p ) Following the field growth for AWAKE-like beams: 8: infinite train of p + bunches (  r =c/  p ) 9: infinite train of p - bunches (  r =c/  p ) Theories: a: 1d theory (Rosenbluth & Liu, 1972) b: 1d theory (Akhiezer & Polovin, 1956) c: approximating parabola

5. presented by K.Lotov at AWAKE collaboration meeting, Duesseldorf 21.06.2013 Why the wakefield period is not 2  c/  p ? Effects of plasma current and wave drive are seen from 8 & 9: not dominating for hundreds of bunches Changing the driver current: 1: very wide single p + bunch (  r =15 c/  p ) 2: wide single p + bunch (  r =3 c/  p ) 3: single p + bunch (  r =c/  p ) 4: 5 normal p + bunches (  r =c/  p ) 5: 5 normal p - bunches (  r =c/  p ) 6: 5 narrow p + bunches (  r =0.3 c/  p ) 7: 5 narrow p - bunches (  r =0.3 c/  p ) Following the field growth for AWAKE-like beams: 8: infinite train of p + bunches (  r =c/  p ) 9: infinite train of p - bunches (  r =c/  p ) Theories: a: 1d theory (Rosenbluth & Liu, 1972) b: 1d theory (Akhiezer & Polovin, 1956) c: approximating parabola plasma current driven wave

6. presented by K.Lotov at AWAKE collaboration meeting, Duesseldorf 21.06.2013 Why the wakefield period is not 2  c/  p ? Wave nonlinearity: depends on driver shape, changes with distance; a universal theory is hardly possible; we will approximate it: Changing the driver current: 1: very wide single p + bunch (  r =15 c/  p ) 2: wide single p + bunch (  r =3 c/  p ) 3: single p + bunch (  r =c/  p ) 4: 5 normal p + bunches (  r =c/  p ) 5: 5 normal p - bunches (  r =c/  p ) 6: 5 narrow p + bunches (  r =0.3 c/  p ) 7: 5 narrow p - bunches (  r =0.3 c/  p ) Following the field growth for AWAKE-like beams: 8: infinite train of p + bunches (  r =c/  p ) 9: infinite train of p - bunches (  r =c/  p ) Theories: a: 1d theory (Rosenbluth & Liu, 1972) b: 1d theory (Akhiezer & Polovin, 1956) c: approximating parabola

7. presented by K.Lotov at AWAKE collaboration meeting, Duesseldorf 21.06.2013 Note on 1d theories 1d wave has fewer degrees of freedom and can be described in a universal way. However, two different results can be found in literature: Rosenbluth & Liu, 1972: + Harley, 1972:

8. presented by K.Lotov at AWAKE collaboration meeting, Duesseldorf 21.06.2013 Note on 1d theories Changing the driver current: 1: very wide single p + bunch (  r =15 c/  p ) 2: wide single p + bunch (  r =3 c/  p ) 3: single p + bunch (  r =c/  p ) 4: 5 normal p + bunches (  r =c/  p ) 5: 5 normal p - bunches (  r =c/  p ) Theories: a: 1d theory (Rosenbluth & Liu, 1972) b: 1d theory (Akhiezer & Polovin, 1956) Akhiezer & Polovin, 1956; Gorbunov, Mora, Ramazashvili, 2002: correct – correct – correct – correct – correct

9. presented by K.Lotov at AWAKE collaboration meeting, Duesseldorf 21.06.2013 Note on 1d theories Rosenbluth & Liu, 1972: The difference comes from the assumption which was taken as obvious Not valid if we take into account the backward drift of plasma electrons (relativistic effect) The drift required for the relative shortening of the wave period by Displacement of a plasma electron (this particular wave is excited by a single short bunch, there is no plasma current) The corner-stone limit for plasma beatwave accelerators is not fully correct:

10. presented by K.Lotov at AWAKE collaboration meeting, Duesseldorf 21.06.2013 Consequence of wave period elongation (consistent with numerical observations)

11. presented by K.Lotov at AWAKE collaboration meeting, Duesseldorf 21.06.2013 To conclude: Strong wakefields can be excited by long trains of equidistant bunches. For realistic beams, these fields are ~40% of the wavebreaking limit. The maximum wakefied weakly depends on contributions of single bunches.

12. Thank you