Shock Ion Acceleration andSolitary Acoustic Wave Acceleration

in Laser-Plasma Interactions

F. Pegoraro, A.S. Nindrayog, A. Macchi

1Department of Physics “Enrico Fermi”, University of PisaLargo Bruno Pontecorvo 3, I-56127 Pisa, Italy

2Istituto Nazionale di Ottica, Consiglio Nazionale delle Ricerche (CNR/INO)Research Unit “Adriano Gozzini”, Pisa, Italy

Bologna, November 2011

The basic idea of ion Shock Acceleration - I

A superintense laser pulse incident on an overdense plasma(ω < ωp, i.e. ne > nc = meω2/4πe2)

heats up electrons up to high (possibly relativistic)temperaturespushes the laser-plasma surface at the “hole boring”velocity

υhb = a0c(

ZA

me

mp

nc

ne

)1/2

a0 = 0.85(

Iλ 2

1018 W cm−2

)1/2

High temperature + strong piston (hopefully) drives a

Collisionless Electrostatic Shock Wave

The basic idea of ion Shock Acceleration - I

A superintense laser pulse incident on an overdense plasma(ω < ωp, i.e. ne > nc = meω2/4πe2)

heats up electrons up to high (possibly relativistic)temperaturespushes the laser-plasma surface at the “hole boring”velocity

υhb = a0c(

ZA

me

mp

nc

ne

)1/2

a0 = 0.85(

Iλ 2

1018 W cm−2

)1/2

High temperature + strong piston (hopefully) drives a

Collisionless Electrostatic Shock Wave

The basic idea of ion Shock Acceleration - I

A superintense laser pulse incident on an overdense plasma(ω < ωp, i.e. ne > nc = meω2/4πe2)

heats up electrons up to high (possibly relativistic)temperaturespushes the laser-plasma surface at the “hole boring”velocity

υhb = a0c(

ZA

me

mp

nc

ne

)1/2

a0 = 0.85(

Iλ 2

1018 W cm−2

)1/2

High temperature + strong piston (hopefully) drives a

Collisionless Electrostatic Shock Wave

The basic idea of ion Shock Acceleration - I

A superintense laser pulse incident on an overdense plasma(ω < ωp, i.e. ne > nc = meω2/4πe2)

heats up electrons up to high (possibly relativistic)temperaturespushes the laser-plasma surface at the “hole boring”velocity

υhb = a0c(

ZA

me

mp

nc

ne

)1/2

a0 = 0.85(

Iλ 2

1018 W cm−2

)1/2

High temperature + strong piston (hopefully) drives a

Collisionless Electrostatic Shock Wave

The basic idea of Shock Acceleration - II

According to standard theory (D. A. Tidman and N. A. Krall, ShockWaves in Collisionless Plasmas (Wiley/Interscience, New York, 1971),chap. 6.)

a Collisionless Shock of velocity υs is preceded by“reflected” ions of velocity υi = 2υs (energy extraction)note that for cs < υs < 1.6cs a non-reflecting ion acousticsoliton may exist, cs = (Te/me)

1/2

If υs & υhb the reflected ions have high (> MeV) energy and aremonochromatic (if υs is constant); an appealing and possiblydominant ion acceleration mechanism[L.O.Silva et al, Phys. Rev. Lett. 92, 015002 (2004)]

The basic idea of Shock Acceleration - II

According to standard theory (D. A. Tidman and N. A. Krall, ShockWaves in Collisionless Plasmas (Wiley/Interscience, New York, 1971),chap. 6.)

a Collisionless Shock of velocity υs is preceded by“reflected” ions of velocity υi = 2υs (energy extraction)note that for cs < υs < 1.6cs a non-reflecting ion acousticsoliton may exist, cs = (Te/me)

1/2

If υs & υhb the reflected ions have high (> MeV) energy and aremonochromatic (if υs is constant); an appealing and possiblydominant ion acceleration mechanism[L.O.Silva et al, Phys. Rev. Lett. 92, 015002 (2004)]

The basic idea of Shock Acceleration - II

According to standard theory (D. A. Tidman and N. A. Krall, ShockWaves in Collisionless Plasmas (Wiley/Interscience, New York, 1971),chap. 6.)

a Collisionless Shock of velocity υs is preceded by“reflected” ions of velocity υi = 2υs (energy extraction)note that for cs < υs < 1.6cs a non-reflecting ion acousticsoliton may exist, cs = (Te/me)

1/2

If υs & υhb the reflected ions have high (> MeV) energy and aremonochromatic (if υs is constant); an appealing and possiblydominant ion acceleration mechanism[L.O.Silva et al, Phys. Rev. Lett. 92, 015002 (2004)]

The basic idea of Shock Acceleration - II

According to standard theory (D. A. Tidman and N. A. Krall, ShockWaves in Collisionless Plasmas (Wiley/Interscience, New York, 1971),chap. 6.)

a Collisionless Shock of velocity υs is preceded by“reflected” ions of velocity υi = 2υs (energy extraction)note that for cs < υs < 1.6cs a non-reflecting ion acousticsoliton may exist, cs = (Te/me)

1/2

If υs & υhb the reflected ions have high (> MeV) energy and aremonochromatic (if υs is constant); an appealing and possiblydominant ion acceleration mechanism[L.O.Silva et al, Phys. Rev. Lett. 92, 015002 (2004)]

Short-pulse driven “Solitary Acoustic Wave”

1D PIC simulation: short (τ = 4T ), intense (a0 = 16),linearly polarized laser pulseon an overdense (ne = 20nc), cold (Ti = 0) protonplasma slab with thickness 15λ .

Short-pulse driven “Solitary Acoustic Wave”

It looks like a soliton . . .

Short-pulse driven “Solitary Acoustic Wave”

. . . but occasionally reflects a short bunch of ions!

Short-pulse driven “Solitary Acoustic Wave”

Short-pulse driven “Solitary Acoustic Wave”

Short-pulse driven “Solitary Acoustic Wave”

Acceleration is “pulsed”, solitary wave almost stays unchanged

Short-pulse driven “Solitary Acoustic Wave”

Short-pulse driven “Solitary Acoustic Wave”

Short-pulse driven “Solitary Acoustic Wave”

Eventually a long-lasting “shock-like” reflection occurs . . .

Short-pulse driven “Solitary Acoustic Wave”

Short-pulse driven “Solitary Acoustic Wave”

. . . and the solitary wave damps out

Short-pulse driven “Solitary Acoustic Wave”

Evolution of ion spectrum

Monoenergetic peak smears out as the solitary wave damps(reflection from a moving, slowing down wall)

Our understanding

For cold ions a a genuine shock wave cannot form (itcannot “pick up” a fraction of “resonant” ions for thereflected trail)A solitary wave can reflect ions as short-duration,small-number, monoenergetic bunches, otherwise it dampsattempting to reflect all background ions

Hint: the ion distribution plays an important part

Our understanding

For cold ions a a genuine shock wave cannot form (itcannot “pick up” a fraction of “resonant” ions for thereflected trail)A solitary wave can reflect ions as short-duration,small-number, monoenergetic bunches, otherwise it dampsattempting to reflect all background ions

Hint: the ion distribution plays an important part

Our understanding

For cold ions a a genuine shock wave cannot form (itcannot “pick up” a fraction of “resonant” ions for thereflected trail)A solitary wave can reflect ions as short-duration,small-number, monoenergetic bunches, otherwise it dampsattempting to reflect all background ions

Hint: the ion distribution plays an important part

Hot ions: steady ion reflection

Same 1D PIC simulation, but now Ti = 5 keV

Hot ions: steady ion reflection

Hot ions: steady ion reflection

Hot ions: steady ion reflection

Hot ions: steady ion reflection

Hot ions: steady ion reflection

It looks like a shock which steadily reflects ions . . .

Hot ions: steady ion reflection

Hot ions: steady ion reflection

Hot ions: steady ion reflection

. . . slowing down in time a bit and broadening the spectrum

Hot ions: steady ion reflection

Hot ions: steady ion reflection

Hot ions: steady ion reflection

Hot ions: steady ion reflection

Oscillations of the solitary wave field

Red: max(Ex)> 0 Blue: min(Ex)> 0

Oscillation mode: collective motion of the electron cloud acrossthe ion density spike

Solitary wave breaking in expanding sheath

Shorter slab: solitary wave reaches rear side sheath

Solitary wave breaking in expanding sheath

Solitary wave breaking in expanding sheath

Solitary wave breaking in expanding sheath

Solitary wave breaking in expanding sheath

Solitary wave breaking in expanding sheath

Solitary wave breaking in expanding sheath

Solitary wave breaking in expanding sheath

Wave breaks at “resonant” point[see also Zhidkov et al, Phys. Rev. Lett. 89, 215002 (2002)]

Long pulse

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

Long pulse

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

Long pulse

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

Long pulse

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

Long pulse

Ions trapped and “surfing” in the multi-peak electric field

Long pulse

Higher density

Long pulse

Long pulse

Long pulse

Long pulse

Long pulse

Long pulse

Long pulse

Lower density

Long pulse

Long pulse

Long pulse

Long pulse

Long pulse

Long pulse

Long pulse

Initial wide bump from front side

Conclusions

Short-pulse, superintense laser interaction with overdenseplasmas may generate collisionless shocks, solitons, orsomething “hybrid”: a solitary wave with pulsed reflectionof ionsThe initial ion distribution plays an important partMonoenergeticity might be at odd with efficiency: largenumbers of reflected ions lead to wave loading and slowingdownFor long pulses we see pulsed acceleration and theproduction of a sequence of electrostatic solitons which“interact” as some ions bounce between adjacent peaks.

Conclusions

Short-pulse, superintense laser interaction with overdenseplasmas may generate collisionless shocks, solitons, orsomething “hybrid”: a solitary wave with pulsed reflectionof ionsThe initial ion distribution plays an important partMonoenergeticity might be at odd with efficiency: largenumbers of reflected ions lead to wave loading and slowingdownFor long pulses we see pulsed acceleration and theproduction of a sequence of electrostatic solitons which“interact” as some ions bounce between adjacent peaks.

Conclusions

Short-pulse, superintense laser interaction with overdenseplasmas may generate collisionless shocks, solitons, orsomething “hybrid”: a solitary wave with pulsed reflectionof ionsThe initial ion distribution plays an important partMonoenergeticity might be at odd with efficiency: largenumbers of reflected ions lead to wave loading and slowingdownFor long pulses we see pulsed acceleration and theproduction of a sequence of electrostatic solitons which“interact” as some ions bounce between adjacent peaks.

Conclusions

Short-pulse, superintense laser interaction with overdenseplasmas may generate collisionless shocks, solitons, orsomething “hybrid”: a solitary wave with pulsed reflectionof ionsThe initial ion distribution plays an important partMonoenergeticity might be at odd with efficiency: largenumbers of reflected ions lead to wave loading and slowingdownFor long pulses we see pulsed acceleration and theproduction of a sequence of electrostatic solitons which“interact” as some ions bounce between adjacent peaks.