Shock Ion Acceleration and Solitary Acoustic Wave Acceleration in Laser-Plasma Interactions

Transcription

1 Shock Ion Acceleration and Solitary Acoustic Wave Acceleration in Laser-Plasma Interactions F. Pegoraro, A.S. Nindrayog, A. Macchi 1 Department of Physics Enrico Fermi, University of Pisa Largo Bruno Pontecorvo 3, I Pisa, Italy 2 Istituto Nazionale di Ottica, Consiglio Nazionale delle Ricerche (CNR/INO) Research Unit Adriano Gozzini, Pisa, Italy Bologna, November 2011

2 The basic idea of ion Shock Acceleration - I A superintense laser pulse incident on an overdense plasma (ω < ω p, i.e. n e > n c = m e ω 2 /4πe 2 ) heats up electrons up to high (possibly relativistic) temperatures pushes the laser-plasma surface at the hole boring velocity ( Z υ hb = a 0 c A m e n c m p n e ) 1/2 a 0 = 0.85( Iλ W cm 2 ) 1/2 High temperature + strong piston (hopefully) drives a Collisionless Electrostatic Shock Wave

3 The basic idea of ion Shock Acceleration - I A superintense laser pulse incident on an overdense plasma (ω < ω p, i.e. n e > n c = m e ω 2 /4πe 2 ) heats up electrons up to high (possibly relativistic) temperatures pushes the laser-plasma surface at the hole boring velocity ( Z υ hb = a 0 c A m e n c m p n e ) 1/2 a 0 = 0.85( Iλ W cm 2 ) 1/2 High temperature + strong piston (hopefully) drives a Collisionless Electrostatic Shock Wave

4 The basic idea of ion Shock Acceleration - I A superintense laser pulse incident on an overdense plasma (ω < ω p, i.e. n e > n c = m e ω 2 /4πe 2 ) heats up electrons up to high (possibly relativistic) temperatures pushes the laser-plasma surface at the hole boring velocity ( Z υ hb = a 0 c A m e n c m p n e ) 1/2 a 0 = 0.85( Iλ W cm 2 ) 1/2 High temperature + strong piston (hopefully) drives a Collisionless Electrostatic Shock Wave

5 The basic idea of ion Shock Acceleration - I A superintense laser pulse incident on an overdense plasma (ω < ω p, i.e. n e > n c = m e ω 2 /4πe 2 ) heats up electrons up to high (possibly relativistic) temperatures pushes the laser-plasma surface at the hole boring velocity ( Z υ hb = a 0 c A m e n c m p n e ) 1/2 a 0 = 0.85( Iλ W cm 2 ) 1/2 High temperature + strong piston (hopefully) drives a Collisionless Electrostatic Shock Wave

6 The basic idea of Shock Acceleration - II According to standard theory (D. A. Tidman and N. A. Krall, Shock Waves in Collisionless Plasmas (Wiley/Interscience, New York, 1971), chap. 6.) a Collisionless Shock of velocity υ s is preceded by reflected ions of velocity υ i = 2υ s (energy extraction) note that for c s < υ s < 1.6c s a non-reflecting ion acoustic soliton may exist, c s = (T e /m e ) 1/2 If υ s υ hb the reflected ions have high (> MeV) energy and are monochromatic (if υ s is constant); an appealing and possibly dominant ion acceleration mechanism [L.O.Silva et al, Phys. Rev. Lett. 92, (2004)]

7 The basic idea of Shock Acceleration - II According to standard theory (D. A. Tidman and N. A. Krall, Shock Waves in Collisionless Plasmas (Wiley/Interscience, New York, 1971), chap. 6.) a Collisionless Shock of velocity υ s is preceded by reflected ions of velocity υ i = 2υ s (energy extraction) note that for c s < υ s < 1.6c s a non-reflecting ion acoustic soliton may exist, c s = (T e /m e ) 1/2 If υ s υ hb the reflected ions have high (> MeV) energy and are monochromatic (if υ s is constant); an appealing and possibly dominant ion acceleration mechanism [L.O.Silva et al, Phys. Rev. Lett. 92, (2004)]

8 The basic idea of Shock Acceleration - II According to standard theory (D. A. Tidman and N. A. Krall, Shock Waves in Collisionless Plasmas (Wiley/Interscience, New York, 1971), chap. 6.) a Collisionless Shock of velocity υ s is preceded by reflected ions of velocity υ i = 2υ s (energy extraction) note that for c s < υ s < 1.6c s a non-reflecting ion acoustic soliton may exist, c s = (T e /m e ) 1/2 If υ s υ hb the reflected ions have high (> MeV) energy and are monochromatic (if υ s is constant); an appealing and possibly dominant ion acceleration mechanism [L.O.Silva et al, Phys. Rev. Lett. 92, (2004)]

9 The basic idea of Shock Acceleration - II According to standard theory (D. A. Tidman and N. A. Krall, Shock Waves in Collisionless Plasmas (Wiley/Interscience, New York, 1971), chap. 6.) a Collisionless Shock of velocity υ s is preceded by reflected ions of velocity υ i = 2υ s (energy extraction) note that for c s < υ s < 1.6c s a non-reflecting ion acoustic soliton may exist, c s = (T e /m e ) 1/2 If υ s υ hb the reflected ions have high (> MeV) energy and are monochromatic (if υ s is constant); an appealing and possibly dominant ion acceleration mechanism [L.O.Silva et al, Phys. Rev. Lett. 92, (2004)]

10 Short-pulse driven Solitary Acoustic Wave 1D PIC simulation: short (τ = 4T ), intense (a 0 = 16), linearly polarized laser pulse on an overdense (n e = 20n c ), cold (T i = 0) proton plasma slab with thickness 15λ.

11 Short-pulse driven Solitary Acoustic Wave It looks like a soliton...

12 Short-pulse driven Solitary Acoustic Wave... but occasionally reflects a short bunch of ions!

13 Short-pulse driven Solitary Acoustic Wave

14 Short-pulse driven Solitary Acoustic Wave

15 Short-pulse driven Solitary Acoustic Wave Acceleration is pulsed, solitary wave almost stays unchanged

16 Short-pulse driven Solitary Acoustic Wave

17 Short-pulse driven Solitary Acoustic Wave

18 Short-pulse driven Solitary Acoustic Wave Eventually a long-lasting shock-like reflection occurs...

19 Short-pulse driven Solitary Acoustic Wave

20 Short-pulse driven Solitary Acoustic Wave... and the solitary wave damps out

21 Short-pulse driven Solitary Acoustic Wave

22 Evolution of ion spectrum Monoenergetic peak smears out as the solitary wave damps (reflection from a moving, slowing down wall)

23 Our understanding For cold ions a a genuine shock wave cannot form (it cannot pick up a fraction of resonant ions for the reflected trail) A solitary wave can reflect ions as short-duration, small-number, monoenergetic bunches, otherwise it damps attempting to reflect all background ions Hint: the ion distribution plays an important part

24 Our understanding For cold ions a a genuine shock wave cannot form (it cannot pick up a fraction of resonant ions for the reflected trail) A solitary wave can reflect ions as short-duration, small-number, monoenergetic bunches, otherwise it damps attempting to reflect all background ions Hint: the ion distribution plays an important part

25 Our understanding For cold ions a a genuine shock wave cannot form (it cannot pick up a fraction of resonant ions for the reflected trail) A solitary wave can reflect ions as short-duration, small-number, monoenergetic bunches, otherwise it damps attempting to reflect all background ions Hint: the ion distribution plays an important part

26 Hot ions: steady ion reflection Same 1D PIC simulation, but now T i = 5 kev

27 Hot ions: steady ion reflection

28 Hot ions: steady ion reflection

29 Hot ions: steady ion reflection

30 Hot ions: steady ion reflection

31 Hot ions: steady ion reflection It looks like a shock which steadily reflects ions...

32 Hot ions: steady ion reflection

33 Hot ions: steady ion reflection

34 Hot ions: steady ion reflection... slowing down in time a bit and broadening the spectrum

35 Hot ions: steady ion reflection

36 Hot ions: steady ion reflection

37 Hot ions: steady ion reflection

38 Hot ions: steady ion reflection

39 Oscillations of the solitary wave field Red: max(e x ) > 0 Blue: min(e x ) > 0 Oscillation mode: collective motion of the electron cloud across the ion density spike

40 Solitary wave breaking in expanding sheath Shorter slab: solitary wave reaches rear side sheath

41 Solitary wave breaking in expanding sheath

42 Solitary wave breaking in expanding sheath

43 Solitary wave breaking in expanding sheath

44 Solitary wave breaking in expanding sheath

45 Solitary wave breaking in expanding sheath

46 Solitary wave breaking in expanding sheath

47 Solitary wave breaking in expanding sheath Wave breaks at resonant point [see also Zhidkov et al, Phys. Rev. Lett. 89, (2002)]

48 Long pulse We now consider a simulation with identical parameters (cold ions), but the duration of the laser pulse is longer: 5T rise and fall ramps and 15T plateau. We observe the generation of a multi-peak structure The reflection of ions from the wave front is not continuous. Loop-like structures corresponding to trapped ions bouncing between adjacent peaks are formed.

49 Long pulse We now consider a simulation with identical parameters (cold ions), but the duration of the laser pulse is longer: 5T rise and fall ramps and 15T plateau. We observe the generation of a multi-peak structure The reflection of ions from the wave front is not continuous. Loop-like structures corresponding to trapped ions bouncing between adjacent peaks are formed.

50 Long pulse We now consider a simulation with identical parameters (cold ions), but the duration of the laser pulse is longer: 5T rise and fall ramps and 15T plateau. We observe the generation of a multi-peak structure The reflection of ions from the wave front is not continuous. Loop-like structures corresponding to trapped ions bouncing between adjacent peaks are formed.

51 Long pulse We now consider a simulation with identical parameters (cold ions), but the duration of the laser pulse is longer: 5T rise and fall ramps and 15T plateau. We observe the generation of a multi-peak structure The reflection of ions from the wave front is not continuous. Loop-like structures corresponding to trapped ions bouncing between adjacent peaks are formed.

52 Long pulse Ions trapped and surfing in the multi-peak electric field

53 Long pulse Higher density

54 Long pulse

55 Long pulse

56 Long pulse

57 Long pulse

58 Long pulse

59 Long pulse

60 Long pulse Lower density

61 Long pulse

62 Long pulse

63 Long pulse

64 Long pulse

65 Long pulse

66 Long pulse

67 Long pulse Initial wide bump from front side

68 Conclusions Short-pulse, superintense laser interaction with overdense plasmas may generate collisionless shocks, solitons, or something hybrid : a solitary wave with pulsed reflection of ions The initial ion distribution plays an important part Monoenergeticity might be at odd with efficiency: large numbers of reflected ions lead to wave loading and slowing down For long pulses we see pulsed acceleration and the production of a sequence of electrostatic solitons which interact as some ions bounce between adjacent peaks.

69 Conclusions Short-pulse, superintense laser interaction with overdense plasmas may generate collisionless shocks, solitons, or something hybrid : a solitary wave with pulsed reflection of ions The initial ion distribution plays an important part Monoenergeticity might be at odd with efficiency: large numbers of reflected ions lead to wave loading and slowing down For long pulses we see pulsed acceleration and the production of a sequence of electrostatic solitons which interact as some ions bounce between adjacent peaks.

70 Conclusions Short-pulse, superintense laser interaction with overdense plasmas may generate collisionless shocks, solitons, or something hybrid : a solitary wave with pulsed reflection of ions The initial ion distribution plays an important part Monoenergeticity might be at odd with efficiency: large numbers of reflected ions lead to wave loading and slowing down For long pulses we see pulsed acceleration and the production of a sequence of electrostatic solitons which interact as some ions bounce between adjacent peaks.

71 Conclusions Short-pulse, superintense laser interaction with overdense plasmas may generate collisionless shocks, solitons, or something hybrid : a solitary wave with pulsed reflection of ions The initial ion distribution plays an important part Monoenergeticity might be at odd with efficiency: large numbers of reflected ions lead to wave loading and slowing down For long pulses we see pulsed acceleration and the production of a sequence of electrostatic solitons which interact as some ions bounce between adjacent peaks.