peter norreys central laser facility laser-plasma interactions reference material: “physics of...

Peter NorreysCentral Laser Facility

Laser-plasma interactionsReference material:

“Physics of laser-plasma interactions” by W.L.Kruer

“Scottish Universities Summer School Series on Laser Plasma Interactions”number 1 edited by R. A. Cairns and J.J.Sandersonnumber 2 edited by R. A. Cairns number 3 - 5 edited by M.B. Hooper

Outline

1. IntroductionIonisation processes

1. Laser pulse propagation in plasmasResonance absorptionInverse bremsstrahlungNot-so-resonant resonance absorption (Brunel effect)

3. Ponderomotive force

4. Instabilities in laser-produced plasmas Stimulated Raman scatter (SRS) instabilityStimulated Brillouin scatter (SBS) instabilityTwo plasmon decayFilamentation

Structure of a laser produced plasma

Laser systems at the CLF

• Laser systems for laser

plasma research

Vulcan: Nd: glass system

• long pulse (100ps-2ns),

2.5 kJ, 8 beams

• 100TW pulse (1ps) and

10TW pulse (10ps)

synchronised with long pulse

• Petawatt (500fs, 500J)

• Upgrading to 10 PW

peak power

8 Beam CPA Laser3 Target Areas3 kJ Energy1 PW Power

UK Flagship 2002-2008: Vulcan facility

Increased complexity, accuracy & rep-rateIncreased complexity, accuracy & rep-rate

UK Flagship 2008-2013: Astra-Gemini facility

Dual Beam Petawatt Upgrade of Astra (factor 40 power upgrade) 1022 W/cm2 on target irradiation 1 shot every 20 seconds Opened by the UK Science Minister (Ian Pearson MP) Dec 07 Significantly over-subscribed. Assessing need for 2nd target area.

Ian Pearson, MPMinister of State for Science and Innovation , Dec 2007

The next step: Vulcan 10 PW (>1023 W/cm2)

100 fold intensity enhancement

OPCPA design

Coupled to existing PW and long pulse beams

104

109

1011 Avalanche breakdown in air

1013 Non-linear optics regime

1014 Tunnel ionisation regime for hydrogen

1015 Scattering instabilities (SRS, SBS etc) become important

1016

3 1016

1017 Self focusing

2 1018 Relativistic effects particle acceleration

1020

1021

Non-linear optics (2nd harmonic generation)

Collisional absorption

Resonance absorption

Profile steepening

Brunel heatingHole boring

Dielectric breakdown (collisional ionisation)

SOLIDS GASES

Introduction

1PW = 1015W

Power = Energy = 500 J = 11015 W

pulse duration 500 fs

To maximise the intensity on target, the beam must be focused to a

small spot.

The focal spot diameter is 7 m and is focused with an f/3.1 off-axis

parabolic mirror. 30% or the laser energy is within the focal spot

which means

Intensity = Power = 1x 1021 W cm-2

Focused area

Vulcan

diffraction gratings

Power and Intensity

Units

In these lecture notes, the units are defined in cgs. Conversions to SI units are given here in the hand-outs.

But note that in the literature

Energy – JoulesPulse duration - ns nanoseconds 10-9 sec (ICF)

ps picoseconds 10-12 sec fs femtoseconds 10-15 sec (limit of optical pulses)as attoseconds 10-18 sec (X-ray regime)

Distance – microns (m)

Power – Gigawatts 109 Watts Intensity – W cm-2

Terawatts 1012 Watts Irradiance – W cm-2 m2

Petawatts 1015 Watts Pressure – Mbar – 1011 PaExawatts 1018 Watts Magnetic field – MG – 100 T

http://wwppd.nrl.navy.mil/formulary/NRL_FORMULARY_07.pdf

• The laser can propagate in a plasma until what is known as the critical density surface. The dispersion relationship for electromagnetic waves in a plasma is so that when = pe the wave cannot propagate

2222 ckpe

Critical density

ncritical = 1.1 1021 cm-3

m2

m is the laser wavelength in m

• An electron oscillates in a plane electromagnetic wave according to the Lorentz force . Neglecting the vB term, then the quiver velocity vosc is

)( BvcEeF 1

meE

v Losc

cv

a osc• The dimensionless vector potential is defined as

Note that a can be > 1. This is because a = = velectron / a and2/1

218

2

104.1

Wcm

Ia

~ 1 if relativity is important and

2/12 ]1[ aelectron

Critical density and the quiver velocity

• The ratio of the quiver energy to the thermal energy of the plasma is given by

eVTI

kTmvosc

2182 1081

2

.

< 1 for ICF plasmas>> 1 for relativistic intensities

• The laser electric field is given by

11000 10

23 Vcma

E.

• The Debye length D for a laser-produced plasma is ~ m for gas targets and ~ nm for solids. n D - 50 -100

• Strongly coupled plasma regime can be accessed

Laser-plasmas can access the high energy density regime

Outline


2. Laser pulse propagation in plasmasResonance absorptionInverse bremsstrahlungNot-so-resonant resonance absorption (Brunel effect)



Ionisation processes

• Multi-photon ionisationNon linear processVery low rateScales as In n = number of photons

• Collisional ionisation (avalanche ionisation)

Seeded by multiphoton ionisationCollisions of electrons and neutrals plasma

•Tunnel and field ionisation

2

232

/

ee Tn

Laser electric field “lowers” the Coloumb barrier which confines the electrons in the atom

Tunnelling

Isolated atom Atom in an electric field

Atom in an oscillating field

i.e.

if

TUNNELLING

if MULTIPHOTON IONISATION

[ = 1, I =61013 Wcm-2, 1m, xenon]

1t

1Ip

2 (EZe3)

Keldysh parameter = time to tunnel out / period of laser field

11032

2 21

6

/

.

I

I

eE

mI pp

eE

mIp

2

skin layer

Laser pulseSolid target

Heated region vapour expansion into vacuum

Outline


2. Laser propagation in plasmasResonance absorptionInverse bremsstrahlungNot-so-resonant resonance absorption (Brunel effect)



Ej

4

2pei

The current density can be written where the conductivity is

and epe mne /0

22 4

)exp()( tikEE Start with an electric field of the form (1)

2

2

1

peWhere we have defined the dielectric function of the plasma

Eci

Eci

Ec

B

4

Bci

E

Substituting (1) into Faraday’s law

Substituting (1) and j into Ampere’s lawgives

(2)tB

cE

1

gives

tE

cJ

cB

14

(3)

EM wave propagation in plasma

i.e. 02

22 E

cEE . 0

2

22 E

cE

Taking the curl of Faraday’s law (2) and substituting Ampere’s law (3) with a standard vector identity gives

(4)

EM wave propagation in a plasma with a linear density gradient

Consider plane waves at normal incidence. Assume the density gradient is in the propagation direction Z. This

)(znn 00 ),( z

)exp()()( tizExE (5)

Substituting (5) into (4) gives 02

2

2

2

yxyx Ec

Edzd

,,

0zE

(6)

cnLz

xn )(

We can rewrite the dielectric function as

when and the critical density is

Lz

nxn pe

c

1112

2

)(

2

2

4 em

nc

(7)

Equation (6) can then be written as 012

2

2

2

E

Lz

cdzEd (8)

Change variables )(/

LzLc

31

2

2

Gives whose solution is an Airy function02

2

Ed

Ed

)()()( ii BAE

and are constants determined by the boundary condition matching.

(9)

Physically, E should represent a standing wave for < 0 and to decay at . Since Bi() as , is chosen to = 0. is chosen by matching the E-fields at the interface between the vacuum and the plasma at z=0. This gives = (L/c)2/3. If we assume that L/c >>1 and represent Ai() by the expression

43

21 3241

// cos)(iA (10)

EM wave propagation in a plasma with a linear density gradient continued (1)

Then

43

2

43

2

20

61

cL

icL

icL

zE expexp)/(

)(/

(11)

Now E(z=0) can be represented as the sum of the incident wave with amplitude EFS with a reflected wave with the same amplitude but shifted in phase

)(exp)(

23

410

cL

iEzE FS

Provided that iFSeE

cL 61

2/

(12)

EEFS is the free space value of the incident light and is an arbitrary phase that does not affect

)(/

i

iFS AeE

cL

E61

2

(13)

This function is maximised at = 1 corresponding to (z - L)= -(c2 L / 2)1/3 31312

26363

//max ..

L

cL

EE

FS(valid for L/>>1)(14)

EM wave propagation in a plasma with a linear density gradient continued (2)

Outline





Oblique incidence

sin20xk

sin

cky

0x

cos

ckz

znc

y

x

Since is a function only of z, ky must be conserved and hence and sin)/( cky

cyi

zEEx

sinexp (16)

Reflection of the light occurs when (z) = sin2 . Remember that = (1 – pe

2(z) / 2) and therefore reflection takes place when pe= cos at a

density lower than critical given by ne = nc cos2 .

Substituting (16) into (15) gives 022

2

2

2

)(sin)( zEzcdz

zEd (17)

s-polarised

xEE x 02

2

2

2

2

2

zxx Ez

czE

yE

)(Eqn (4) becomes (15)

Oblique incidence – resonance absorption

p-polarised

In this case, there is a component of the electric field that oscillates along the density gradient direction, i.e. . Part of the incident light is transferred to an electrostatic interaction (electron plasma wave) and is no longer purely electromagnetic.

E. ne 0

This means that there is a resonant response when = 0, i.e. when = pe

We seen previously that the light does not penetrate to nc. Instead,the field penetrates through to = pe

to excite the resonance.

sin2

znc

y

x

zEyEE zy

0 E.(18)

EEE ...

zEz

E

1

.

Remember the vector identity

then (19)

Oblique incidence – resonance absorption continued

B decreases as E gets larger near the reflection point

The B-field can be expressed as

x

cyi

tizBB sinexp

xBB x

sin

ckyNote that the magnetic field and use the conservation of

(20)

Substituting into Ampere’s law (equation (3)) givesEci

B

)()(sin

zE

Bz

E dzz

(21)

This implies that Ez is strongly peaked at the critical density surface and the resonantly driven field Ed is evaluated there by calculating the B-field at nc.

From Faraday’s law or zEic

B

Ez

icB (22)

)(/

i

iFS AeE

cL

E61

2

)(

/

i

iFS AeE

Lc

iB61

2

(23)

At the reflection point, FSELc

B61

900/

.)(

The B field decays like exp (-) where . L

Ldzzk

2cos)(

dzc p

L

L

212222

1 /

coscos

L

zpe 2

2

Solution: 3

3

2sin

cL

sin/31

cL

Defining)(

sin)( z

Bz

EE d

z

and remember that

(24)

(25)

c

L

L

cELzB FS 3

sin2exp9.0)(

36/1

(27)

(26)

)()/(

cLE

E FSd 2

3

3

232 exp.)(

The driver field Ed vanishes as 0, as the component along z varies as sin

Also, Ed becomes very small when , because the incident wave has to tunnel through too large a distance to reach nc

The simple estimate for () from (28) is plotted here against an numerical solution of the wave equation.

Note that the maximum value of () is ~1.2 (needed to estimate the absorption fraction in the next section)

(28)

Resonance absorption – energy transfer

)(zE

E dz Start from the electrostatic component of the

electric field.

)()(

i

z p

2

1Now include a damping term in the dielectric function of the plasma that can arise form collisions, wave particle interactions etc.

For a linear density profile, (ne = ncr z / L)

Substituting and approximating that Ed is constant over a narrow width of the resonance function gives

2

2222 1

Lz

Lz

0 22

2

18

/)/( LzdzLzE

I dabs

The integral gives , 8/2dabs LEI

8

2FS

Aabs

cEfI 22 /Af

dzzE

dzE

I dzabs

0 2

2

0

2

88

)(

can be considered as the rate of energy dissipation and Ez2/8the

incident energy density.

The absorption is maximised at an angle given by

311 80 /max )/(.sin Lc

This is the characteristic signature of resonance absorption – the dependence on both angle of incidence and density scale-length.

Iabs peaks at ~0.5

Outline






Principal energy source for direct drive inertial fusion plasmas

From the Vlasov equation, the linearized force equation for the electron fluid is

eeie uE

me

t

u

where ei is the damping term.

Since the field varies harmonically in time

eie im

Eieu

The plasma current density is Ei

iuenJ

ei

peee )(

4

2

The conductivity (J=E) and dielectric function )( ei

pe

i

i

4

2

)( ei

pe

i

2

1

Eci

B

Bci

E

Faraday’s law (cf (eqn (2))

Ampere’s law (cf eqn (3))

Combining them gives 02

22 E

cE

To derive the dispersion relation for EM waves in a spatially uniform plasma, take

xkiexE .~)( and substitute for and assume that ei/ << 1 gives

)( ei

pe

ick 12222

2/ ir Expressing gives 21222 /ckper

eir

pe

2

2

where is the energy damping term.


collisional damping in linear density gradient

The rate of energy loss from the EM wave [ = (E2/8must balance the oscillatory velocity of the electrons is randomised by electron- ion scattering. Assume again that ne = ncr z / L and write down equation (4) again

02

2

2

2

Ezcz

E)(

The dielectric function (z) is now

/*11

1eiL

z

where *ei

is its value at ncr

01

12

2

2

2

EiLz

cdzEd

ei

/*

Changing variables again, gives Airy’s equation 02

2

Ed

Ed

ei

ei

iLz

iLc1

1

31

2

2 /

/

)()( iAE

43

21 3241

// cos)(iA

Again, match the incident light wave to the vacuum plasma boundary interface at z=0

Thus at z=0, E can be represented as an incident and reflected wave whose amplitude is multiplied by ei

2

03

4 )(z

As is now complex, there is both a phase shift and a damping term for the reflected wave

32

10

/

)(

eii

cL

For ei/ <<1 23

4 cL

real cLei

imaginary 3

4

cL

amplitudeEnergy ei3

82 exp~)(~

cL

f eiA 3

81

exp

123

6103 secln /eV

eei T

Zn

Energy absorption

240

6023

LL

LA I

Zf

.

./

Experiment shows

Outline





Eplasmavacuum

From P.Gibbon Phys. Rev. Lett. 76, 50 (1996)

•Dominant mechanism is L/ < 1

•Quiver motion of the electrons in the field of a p-polarised laser pulse

• Laser energy is absorbed on each cycle

• Can result in higher absorption than classical resonance absorption (up to 0.8)

•Not as dependent on angle

Collisionless “Brunel” absorption

Incidentlight

Reflectedlight frommirror at 0t/2= 0

Reflected light from mirror at 0t/2= 0.5

Harmonic generation: the moving mirror model

see references:D. von der Linde and K. Rzazewski: Applied Physics B 63, 499 (1996).R. Lichters, J. Meyer-ter-Vehn and A. Pukhov Phys. Plasmas 3, 3425 (1996).

z

tst m sincos)2()( 00

is the angle of incidence, m is the modulation frequency. The electric field of the reflected wave is

Ignoring retardation effects, the phase shift of the reflected wave resulting from a sinusoidal displacement of the reflecting surface in the z direction s(t)=s0 sinwmt is

tinn

nn

tititiR

meJeeeE

)(00 )(

)(nJ is the Bessel function of order n and cos)/2( 00 cs

where we’ve made use of the Jacobi expansion

n

n

tintiz mm eJe )(sin

The moving mirror model

5x1017 5x1018 1x1019

Energy conversion efficiencies of 10-6 in X-UV harmonics up to the 68th order were measured and scaled as E() = EL()-q

Good agreement was found with particle in cell simulations

Conversion efficiency dependence on intensity on target

P.A.Norreys et al. Physical Review Letters 76, 1832 (1996)

For I2 = 1.21019 Wcm-2m2

and n/nc = 3.2 only 0 oscillations are observed. The power spectrum extends to ~35 and still shows modulations. Over dense regions of plasma are observed at the peak of the pulse.

I2 = 1.2 1019 Wcm-2m2

and n/nc = 6.0, both 0 and 20 oscillations appear.

Complex dynamics of nc motion

Additional order results in the modulation of the harmonic spectrum

I.Watts et al., Physical Review Letters 88, 155001 (2002).

• Harmonic efficiency changes with increasing density scale-length and mirrors the change in the absorption process

• As the density scale-length increases, the absorption process changes from Brunel-type to classical resonance absorption.

• Maximum absorption at L/~0.2

M. Zepf et al., Physical Review E 58, R5253 (1998).

Intense laser-plasma interaction physics

B.Dromey, M.Zepf….P.A.Norreys Nature Physics 2 546 (2006)

High harmonic generation – towards attosecond interactions

Outline





Ponderomotive force

Neglecting electron pressure, the force equation on the electron fluid is

txEme

uut

uee

e sin)(

txEme

tuh

sin)(

To a first approximation where he uu t

mEe

uh

cos

Averaging the force equation over the rapid oscillations of the electric field,

tuumEetu

m hhss

.

< > denotes the average of the high frequency oscillation, tes uu t

s EE

)(xEme

Eetu

m ss

22

2

4

1

x1x3 x0 x2

• An electron is accelerated from its initial position x0

to the left and stops at position x1.

• It is accelerated to the right until its has passed its initial position x0.

• From that moment, it is decelerated by the reversed electric field and stops at x2

• If x0’ is the position at which the electric field is reversed, then the deceleration interval x2- x0

’

is larger than that of the acceleration since the E field is weaker and a longer distance is needed to take away the energy gained in the former ¼ period.

• On its way back, the electron is stopped at position x3

The result is a drift in the direction of decreasing wave amplitude.

Ponderomotive force

Outline





Summary of laser-plasma instabilities

Stimulated Brillouin Scatter - SBS. Scattered light is downshifted by ia L

Source of large losses for ICF experiments

Very dangerous for laser systems

Stimulated Raman Scatter – SRS. Scattered light downshifted by p

Produces large amplitude plasma waves

Hot electrons (Landau damping)Preheating of fuel

Two Plasmon Decay - TPD. Decays into two plasma waves Not as serious Localised near ncr / 4.

Filamentation Can cause beam non-uniformities problematic for direct drive ICF

ncrit / 4

ncrit

SBS – back and sideSelf focusing and filamentation

TPD

Raman back and side scatter

SRS

psc

iasc

SBS

TPD

pp

Dispersion relation

2

3212222 10

mcrpe

cmnkc

x

n

Regimes of applicability

Large amplitude light wave couples to a density fluctuation

nEL

Drives an electric field associated with an electron plasma wave

pE

The electric fields combine to generate a fluctuation in the field pressure

pLEE

nEnhances the density perturbation

The threshold for the instabilities is determined by spatial inhomogeneities and damping of plasma waves – this reduces the

regions where the waves can resonantly interact

Parametric instability growth

k

photons

plasmons

ion acoustic phonons

Parametric decay

Outline





Stimulated Raman Scatter

pes 0

pes kkk 0

The instability requires pe 20

4crn

ni.e

10 % in ICF plasmas. The instability causes heating of the plasma, due to damping

Can have high phase velocity – produces high energy electrons

k

photons

plasmons

Stimulated Raman scattering

Derive an expression that relates the creation of the scattered EM waves (by coupling the density perturbations generated by the laser field) to the transverse current that produces the scattered light wave.

Start from Ampere’s law tE

cJB

1

4

Remember that 0 A AB

tA

cE

1

tc

jc

Atc

141 22

2

2

AAA 2 ).()(

(1)

(2)

General instability analysis

ltjjj Separate J into a EM part jt and a longitundinal part jl (3)

04

)( jt

Taking t of (4) and substituting for t from (5)

42 Poisson’s equation

Conservation of charge 0

jt

.

is the charge density(4)

(5)

(6)

lj

t 4

0t

j.because (7)

Equation (2) becomes t

jc

Atc

41 22

2

2

(8)

If we restrict the problem to A. ne = 0, the transverse current becomes jt = - ne e ut where ut is vosc. For ut <<c, ut =eA/mc because

tA

mce

Eme

tu

tt

(9)

General instability analysis continued…1

Anme

Act e

222

2

2 4

(10)

Now we need an equation for the density perturbation

0

eee untn

Continuity equation

Force equationmnp

cBu

Eme

uutu

e

eeee

e

(12)

(13)

Here the ions are fixed and provide a neutralising background

Substitute for 1AAA L and ne = n0 + n1

Lpe Anme

Act 1

2

1222

2

2 4

(11)

The right hand side is simply the transverse current ( n1vL ) that produces the light wave.

This gives eqn for propagation of a light wave in a plasma

mcAe

uu Le transverse

longitudinal

(14)

BmcAe

uc

Eme

mnp

mcAe

umcAe

umcAe

ut L

e

eLLL

1

AB

tA

cE

1 2

2

1AAAAA

substituting

givesmnp

mcAe

ume

tu

e

eL

L

2

2

1

Electric field

Ponderomotiveforce

Plasma pressure

(15)


Use adiabatic equation of statepe/ne3 = constant (16)

Linearise (12) and (15). Do this by taking 11 AAAnnnuu LoeL ,,

03

)(e

e

np

1

3n

np

pe

ee

10

23n

nv

mnp th

ee

e

(17)

10

22

11

3

2

1n

nv

AAmce

ume

tu th

L

(18)


To 1st order ignore A12, u1

2 and 01 Au

10

2

122

2 3n

nv

AAcm

eme

tu th

L (19)

0101

untn

. (20)

Combining by taking time derivative of (20), a divergence of (19) gives

12

22

20

1222

2

2

3 AAcmen

nvt Lepe

)(

Where en12 4

(21)

This is now the equation for the density perturbations generated by fluctuations in the intensity of the EM wave

General instability analysis finalised

Dispersion relationship for SRS

Start with )cos( txkAAL 000

0010010

2

12222

2

4 ,),(),( kknkknAme

kAck pe

Fourier analyse

0010010220

22

122

2 ,),(),( kkAkkAA

cmnek

knek

Where is the Bohm-Gross frequency and 0 and k0 are the frequency and wave number of the laser wave. Also

21222 3/

epeek vk

)exp( iwtikxAA 11

)exp( tiikxnn 11

)cos( twxkAA 0000

)](exp)([exp twxkitwxkiAA 000000

(22)

(23)

(24)

Use (19) to eliminate A1

0000

22222 11

4 kkDkkD

vk ospek ,,

vos is the oscillatory velocity (eA0/mc)

Note: in deriving (25), it was assumed that pe and terms n1 (k-2k0, -20) and n1 (k+2k0, +20) were neglected as non-resonant.

(25)

From this dispersion relation, the growth rates can be found. Neglecting the up-shifted light wave as non-resonant gives

4

222222

0

2

022 ospe

peek

vkckk

(26)

2222peckkD ,

Growth rates

Then take iwhere

21

0

2

4

/

ekek

peoskv

Take where . Note that maximum growth rate occurs when the scattered light is resonant, i.e. when

ek ek

02220

20 peek ckk (27)

(28)

The wave number k is given by (27). For backscattered light the growth rate maximises for

21

0

00

21

/

pe

ckk

The wave numbers start at k = 2k0 for n << nc/ 4 and goes to k = k0 for n~ncr/4

(29)

Maximum growth rate

For forward scattered light at low density k<<0/c, both the up-shifted and down-shifted light waves can be nearly resonant

000 2 pekkD ,

Substitute into (25), the maximum growth rate i

cvospe

0

2

22

Growth rate in low density plasmas

(30)

(31)

Outline





k

photons

ion acoustic phonons

Stimulated Brillouin Scatter

Stimulated Brillouin Scattering (SBS)

• density fluctuations associated with high frequency ion acoustic waves causes scattering of light

•> 60 % has been observed in experiment

ias 0

ias kkk 0

Lpe Anm

eAc

t 1

2

1222

2

2 4

• Similar analysis to SRS, except n1 is density fluctuation associated with an ion acoustic wave. We write

• Force equation gives 12

2

20

12

21

2

AAmMc

eZnnc

tn

Ls

21/)/( MZkTc es ion acoustic velocity

(32)

(33)

Fourier analyse (32) and (33)

ikcs

skc

20

0

22

cc

kk c

2100

0

22

1/

s

pios

ck

vk

gives

(34)

(35)

Growth rate

for backscattered light

reflectivity average ion energy

Holhraum irradiation uniformity by SBS

S. Glenzer et al., Science 327, 1228 (2010)P. Michel et al., Phys. Rev. Lett. 102, 025004 (2009)

Outline





Two plasmon decay instability

• Occurs in a narrow density region at ncr / 4

pepe

21 kkk

• Similar analysis as SRS except the equations describe the coupling of the electron plasma waves with wave number and with the large light wave

•For k>>k0, for plasma waves at 45 to both k and vos

• Threshold is much less than SRS at ncr / 4 unless the plasma is hot

k 0kk

40 osvk

k

photons

plasmons

Two plasmon decay

Outline





Filamentation instability

• Same dispersion relation as SBS also describes filamentation

• Zero frequency density perturbation corresponding to modulations of the light intensity

• Occurs in a plane orthogonal to propagation vector of light wave

0 i

0 okk

0

22

8

1

p

t

os

vv

• Filamentation can also be caused by thermal or relativistic effects: 1. enhanced temperature changes refractive index locally

2. relativistic electron mass increase has same effect as reducing the density

GWPpe

critical 2

2

20

for self-focusing

Efficient Raman amplification into the petawatt regime

R. Trines , F. Fiuza, R. Bingham, R.A. Fonseca, L.O.Silva, R.A. Cairns and

P.A. Norreys

Nature Physics 7, 87 (2011)

Raman amplification of laser pulses

•A long laser pulse (pump) in plasma will spontaneously scatter off Langmuir waves: Raman scattering

Stimulate this scattering by sending in a short, counter propagating pulse at the frequency of the scattered light (probe pulse)

Because scattering happens mainly at the location of the probe, most of the energy of the long pump will go into the short probe: efficient pulse compression

Miniature pulse compressor

Solid state compressor (Vulcan)

Volume of a plasma-based compressor

Image: STFC Media Services

Simulations versus theory

RBS growth increases with pump amplitude and plasma density, but so do pump RFS and probe filamentation

Optimal simulation regime corresponds to at most 10 e-foldings for pump RFS and probe filamentation

Growth versus plasma density Growth versus pump amplitude

A bad result

For a 2*1015 W/cm2 pump and ω0/ωp = 10, the probe is still amplified, but also destroyed by filamentation

A good result

For a 2*1015 W/cm2 pump and ω0/ωp = 20, the probe is amplified to 8*1017 W/cm2 after 4 mm of propagation, with limited filamentation10 TW → 2 PW and transversely extensible!

peter norreys central laser facility laser-plasma interactions reference material: “physics of...

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