Fundamental Issues in the Interaction of Intense Lasers with PlasmaNathaniel J. Fisch

Department of Astrophysical Sciences, Princeton University2018 Stewardship Science Academic Programs Symposium, Bethesda, MD, February 21, 2018

Goals1. Identify methods for next generation light intensities

2. Identify new effects in highly compressed plasma

3. Formulate general description of fundamental wave effects

Collaborators at Princeton University: I. Y. Dodin, Q. Jia, K. Qu, and V. M. MalkinCollaborators (not funded by NNSA): J. Mikhailova (Princeton), I. Barth (Hebrew U.)Current graduate students: Y. Shi, M. Edwards, V. Munirov, E. Kolmes

Recent graduates involved in NNSA sponsored research: Z. Toroker *15 (Intel) M. Hay *16 (Volant) V. Geyko *17 (LLNL)D. Ruiz *17 (SNL) S. Davidovits *17 (Princeton)

Paradigm: Plasma as Active Medium Amplifier

Output parameters (unfocused)

Pulse fluence 4 kJ/cm2

Pulse duration 40 fsPulse power 1017 W/cm2

Plasma width 0.7 cmPump duration 50 psPump intensity 1014 W/cm2

Representative parameters

Malkin, Shvets, and Fisch (1999)

Some recent variations

pump plasma

chirped pump graded plasma no seed

Plasma oscillations

seed with sharp front

0 zzi

(a)

(b)

(c)

Moving Laser Seed

Stationary Plasma Seed

Probe Beam

Pump

Pump

Pump

Plasma Wave Seed for Raman Amplifiers

K. Qu, I. Barth, and N. J. Fisch, PRL (April 2017)

f0 (z) c0

z

b0 (z)

Equivalent Greens function linear solution Pump depletion solution asymptotically equivalent

Also, chirping in kequivalent to chirping in

Qu & Fisch, PoP 24, 073108 (July, 2017)

Sharpening seed laser through EIT in plasma

Inhibited transmission absent pump

Advantages: damageless, counterpropagating geometrypulse contrast not limited by ionizationenergy gain

PIC (EPOCH) Demonstration

seed frequency below plasma frequency

Weak Seed Broad Pump

(b)

Transmission

Reflection

(a)

EIT -- Electromagnetically Induced Transparency

Another Possibility: Coupling to the Upper-Hybrid (UH) Wave

• UH wave is magnetized version of Langmuir wave• Dispersion relation of UH wave:

• Polarization of UH wave is approximately longitudinal

By coupling to upper-hybrid wave replace plasma density by B-field.

Lower density mitigates modulational instability, allowing longer propagation.

Resonance more stable, since B more easily uniform than plasma density

Lower density opens n-T window at shorter wavelength.

Y. Shi, H. Qin, and N. J. Fisch (2016)

Three-Wave Scattering in Magnetized Plasmascoupling at arbitrary angles

Y. Shi, H. Qin, and N. J. Fisch (PRE, 2017)

Anisotropic scattering by magnetized wavesAngular dependence previously unknownEnhance /suppress by special angles

MG fields start to affect optical lasers

Three-Wave Scattering in Magnetized Plasmaslaser pump propagating parallel to B

Y. Shi, H. Qin, and N. J. Fisch (PRE, 2017)

Scattering from magnetized Langmuir wave similar to unmagnetizedScattering from cyclotron waves mostly perpendicular ion contribution dominates

Laser-Plasma Interaction in Magnetized Environmentcoherent scattering in general geometry

Y. Shi, H. Qin, and N. J. Fisch (POP, 2017)

Scattering suppressed when:Polarization, energy, and interference forbidden

Scattering enhanced when:Previously small scattering increase to Raman level, away from special angles

Control scattering by angle with MG fields

Radiative Transfer Dynamo Effect

Munirov and Fisch, PRE (January, 2017).

Radiative transfer effects in differentially rotating and radiating atmospheres

Inverse Bremsstrahlung Current Drive

Munirov and Fisch, PRE(November, 2017).

Ion recoil: 8/5 laser momentum captured by electrons (Pashinin and Fedorov, 1978).

Current drive and magnetic dynamo: Kinetic terms dominate.

In progress: inverse-B current drive in Fermi-degenerate plasma.Kinetic effects totally dominate.

Inverse Bremsstrahlung Current Drive

Recoil effect: asymmetric in electron velocity

Large Z limit: I 2.7 I

Very different in Fermi degenerate plasma!

Munirov and Fisch, PRE(November, 2017).

Transverse cooling from 4-wave scattering

zparaxial beam

1 2

3 4

0 vg kz k0 k

2 2k0

1

2k 2

2k 3

2k 4

2kd 2k k

2NkTransverse energy conserves

So small amount of energy goes to large

Most goes to small

k

But at much longer than propagation distances for coherent pulses of the of the same intensity

k

Malkin, Phys. Rev. Lett. 76 , 4524 (1996)

Introduce random inhomogeneities for transverse-k heating

Malkin & Fisch, PRL (September, 2016)

To prevent Bose-Einstein condensation to small and self-focusing choose

k

~ k0 fr L||r z Lr

k

grows with propagation distance z

L||r Lr correlation lengths

fr ~ fluctuation amplitude

LSF = self focusing length at same intensity

LSF fr L||r/ Lr ~ 1

= number of populated scales

k

Randomized Plasma Pulse Compression using 2-stage RBS following Malkin and Fisch (2005)

1

2

first seed3

chirped pump

first plasma (randomized)

second pump

output focusable compressed pulse

~ J/cm2

kJ/cm2

~ 4 fs

second seed

4 5

second (dense and thin) plasmato compress and “beam clean”

first stage output not focusable, but high power, long plasma

Beam Cleaning of an Incoherent Laser via Plasma Raman Amplification

Edwards, Qu, Mikhailova, and Fisch, PoP (October, 2017)

Lower bound on turbulent velocity in compressing turbulence

Robertson & Goldreich, ApJL 750, L31 (2012)

Compressing in timeTurbulent velocity changes under compression

Can amplify or decrease

2017 derivation: Lower bound on turbulent velocity

Davidovits & Fisch, ApJ 838, 118 (2017)

Implication: previous simulation/modeling efforts may be too dissipative

Highlight: importance of condensation to small k (compare: wave nonlinear focusing)

Adiabatic heating of isothermal supersonic turbulence during contraction

Lower Bound

Heat Capacity of spinning plasmaV. I. Geyko and N. J. Fisch, Phys. Plasmas 24, 022113 (2017).

Consider plasma spinning in a cylinder with a smooth wall condition. Heavy particles hug the wall; light particles are distributed more homogeneously. Charge separation creates electrostatic forces that attract particles.

cBxQnnxnEQ

xnnx iii

iii

~~~~21~

BxQnnxnEQxnnx eee

eee

~~~~21~

ei nnxExx

~~~

ei nnxxB ~~~

004~

rqnBB

LrNno20

0

,,

~nn

n eiei

004~

rqnEE

Trm ei

ei 2

20

2,

,

LT

NqT

rmQ pii

220

2 22

cr0 cT

BrqT

rm cii

220

20

20

Self magnetic field effects can be neglected for non-relativistic rotation

Spinning plasma and slab geometry analogy

Plasma rotation near in the vicinity of the boundary is similar to 1D plasma slab motion in constant gravitational field

00 r mgrm 02

Derive spinning plasma thermodynamics for 1D slab geometry

BQnnxnEQznnG iii

iii

~~~~~

~0

BQnnxnEQznnG iee

eee

~~~~~

~0

HqnBB

04~

DHLNn 0

0

,,

~nn

n eiei

HqnEE

04~

TgHm

G eiei

,,

LDTNHq

THm

Q pii222 4

c0 cT

HBqT

Lm cii 000

Self magnetic field effects can be neglected for non‐relativistic motion              1

Slab geometry

Basic equations

ei nnzE ~~~

ei nnzB ~~~

~

Electrostatic energy

Total internal energy

pEkT WWWWU

1

0

2 ~)~(~2

zdzEQNTWE

Slab geometry

NTcTNNcW vievT 2)( Thermal energy

Kinetic energy eiiieeK mmNmNmNW 22

)(20

20

Potential energy 1

0

~~~~eeiiP GnGnzdzNTW

Slab geometry analogy

Heat capacity at constant canonical momentum

constnnzdzHNmNmmP eiciiiec

1

00

~~

Total canonical momentum

00,,

~

cc

PLHv

PTPU

TU

TUc

c

000

dPdT

TP cc

Slab geometry analogy

Heat capacity for             ,  00 B 10/ ei mm

Slab geometry analogy

Heat capacity for positive                ,  900 B 10/ ei mm

Slab geometry analogy

Heat capacity for negative                   ,  900 B 10/ ei mm

Like a particle in a HF field, a photon in a modulated medium has aponderomotive Hamiltonian and polarizability, which are operators.

Ruiz and Dodin, PRA (2017) – Kaleidoscope

The photon susceptibility ph = 4phnph contributes to the dielectrictensor. Theory of "photon Landau damping" beyond geometrical optics:

Dodin and Ruiz, JPP (2017) ‐‐ Featured Article

PRA Kaleidoscope

The interaction of a linear EM wave with a medium described by aquantum‐like variational principle [Dodin et al, PLA (2017)]:

Classical waves behave like quantum particles but without h

Modulation wave in a photon gas 

(cartoon)

Application: Plasmons can be trapped and accelerated by chirped sound

Argued previously based on a linear fluid theory: densitymodulations at (, K) can trap plasmons with g /Kand transport them reversibly up and down in spectrum.Applications: fine‐tuning of the plasmon wave vector k.Barth, Dodin, and Fisch, PRL (2015)

Recent advances: Vlasov‐Maxwell simulations, show thatthis "ladder climbing" survives kinetic and nonlineareffects. In fact, it is even more robust in the nonlinearregime because Landau damping is suppressed.Hara, Barth, Kaminski, Dodin, and Fisch, PRE (2017)

Extension: Mode Conversion Physics 

Recent advances: XGO is formulated for general linear waves. The mode conversion problem for anytwo modes is reduced to the precession equation for a 3D real "spin" vector S:

Ruiz and Dodin, Phys. Plasmas (2017) – invited

Recent application: Analytic calculation of the EMwave transformation in edge stellarator plasma(DOE‐sponsored, in collaboration with NIFS, Japan).

Dodin, Ruiz, and Kubo, Phys. Plasmas (2017) – Editor's Pick

Utility: If Q changes slowly, the precession plane ofS will follow the direction of Q. This allows findingthe final amplitudes robustly without simulations.

Earlier results: extended geometrical optics (XGO) was proposed that captures corrections to thetraditional GO, including mode conversion, for wave equations of a particular type.Ruiz and Dodin, PLA (2015); PRA (2015)

Fundamental Issues in the Interaction of Intense Lasers with Plasma

1. Goal: Achieve next generation of light intensities -- parametric wave compression

a. Sharpening of laser seed through electromagnetically induced transparency.

b. Coupling to UH wave in magnetized plasma – amplification of x-rays

c. Extended amplification in plasma with random inhomogeneities

2. Goal: Identify new wave effects in highly compressing plasma

a. Upper bound on dissipation in compressing plasma.

b. Heat capacity of spinning plasma.

c. Inverse bremsstrahlung current drive and radiative transfer dynamo effect

3. Goal: Generalized Description of Waves in Dense and Relativistic Media

a. Lagrangian description of waves extended, including dissipation & mode conversion

b. Extended propagation of intense lasers in random media

c. General scattering matrix for 3-wave coupling in magnetized plasma

some recent progress

References October 2016 – September 2017 1. I. Barth and N. J. Fisch, Reducing Parametric Backscatter by Polarization Rotation, Physics of Plasma 23, 102106 (October, 2016). 2. V. I. Geyko and N. J. Fisch, Piezo-thermal effect in spinning gas, Physical Review E 94, 042113 (October, 2016). 3. D. E. Ruiz, J. B. Parker, E. L. Shi, and I. Y. Dodin, Zonal-flow dynamics from a phase-space perspective, Phys. Plasma 23, 122304 (Dec.,

2016).4. V. I. Geyko and N. J. Fisch, Compressibility and heat capacity of rotating plasma, Physics of Plasma 24, 022113 (February, 2017). 5. Y. Shi, H. Qin, and N. J. Fisch, Laser Pulse Compression using Magnetized Plasmas, Physical Review E 95, 023211 (February, 2017). 6. R. Gueroult, Y. Ohsawa, and N. J. Fisch, Role of Magnetosonic Solitons in Perpendicular Collisionless Shock Reformation, Physical Review

Letters 118, 125101 (March, 2017).7. D. E. Ruiz and I. Y. Dodin, Ponderomotive dynamics of waves in quasiperiodically modulated media, Phys. Rev. A 95, 032114 (March, 2017);

selected for PRA Kaleidoscope.8. E. J. Kolmes, V. I. Geyko and N. J. Fisch, Heat Pump Model for Ranque-Hilsch Vortex Tube, International Journal of Heat and Mass Transfer

107, 771-777 (April, 2017). 9. I. Y. Dodin and D. E. Ruiz, Photon polarizability and its effect on the dispersion of plasma waves, J. Plasma Phys. 83, 905830201 (April,

2017).10. I. Y. Dodin, A. I. Zhmoginov, and D. E. Ruiz, Variational principles for dissipative (sub)systems, with applications to the theory of linear

dispersion and geometrical optics, Phys. Lett. A 381, 1411 (2017).11. K. Qu, I. Barth, and N. J. Fisch, Plasma Wave Seed for Raman Amplifiers, Physical Review Letters 118, 164801 (April, 2017). 12. M. J. Hay, J. Schiff, and N. J. Fisch, On extreme points of the diffusion polytope, Physica A 473, 225--236 (May, 2017).13. S. Davidovits and N. J. Fisch, A Lower Bound on Adiabatic Heating of Compressed Turbulence for Simulation and Model Validation,

Astrophysical Journal 838, 118 (April, 2017).14. D. E. Ruiz and I. Y. Dodin, Extending geometrical optics: A Lagrangian theory for vector waves, Phys. Plasmas 24, 055704 (May, 2017).15. M. J. Hay, J. Schiff, and N. J. Fisch, On extreme points of the diffusion polytope, Physica A-Statistical Mechanics and its Applications 473,

225-236 (May, 2017).16. K. Hara, I. Barth, E. Kaminski, I. Y. Dodin, and N. J. Fisch, Kinetic simulations of ladder climbing by electron plasma waves, Phys. Rev. E 95,

053212 (July, 2017).17. K. Qu and N. J. Fisch, Laser pulse sharpening with electromagnetically induced transparency in plasma, Phys. Plasmas 24, 073108 (July,

2017).18. Y. Shi and H. Qin, and N. J. Fisch, Three-wave scattering in magnetized plasmas: From cold fluid to quantized Lagrangian, Physical Review

E 96, 023204 (2017).19. M. R. Edwards, J. M. Mikhailova, and N. J. Fisch, X-ray amplification by stimulated Brillouin scattering, Physical Review E 96, 023209

(August, 2017).20. Q. Jia, Y. Shi, H. Qin, and N. J. Fisch, Kinetic simulations of laser parametric amplification in magnetized plasmas, Physics of Plasmas 24,

093103 (September, 2017).

1. M. R. Edwards, J. M. Mikhailova, , K. Qu, and N. J. Fisch, Beam Cleaning of an Incoherent Laser via Plasma Raman Amplification, Physics of Plasmas 24, 103110 (October, 2017).

2. K. Qu, Q. Jia, and N. J. Fisch, Plasma q-plate for generation and manipulation of intense optical vortices, Physical Review E 96, 053207 (November, 2017).

3. V. R. Munirov and N. J. Fisch Inverse Bremsstrahlung current drive, Phys. Rev. E 96, 053211 (November, 2017).4. Y. Shi and H. Qin, and N. J. Fisch, Laser-plasma interaction in magnetized environment, to appear in Physics of Plasmas (2018).

Theses (October 2016 – September 2017; NNSA acknowledged)

Michael J. Hay, On the Utility of Nonthermal Plasmas,Ph.D. Thesis, submitted to Department of Astrophysical Sciences, Princeton University (November, 2016).Advisor N. J. Fisch

Vasily I. Geyko, Physics of spinning gases and plasmas,Ph.D. Thesis, submitted to Department of Astrophysical Sciences, Princeton University (January, 2017).Advisor N. J. Fisch

Daniel E. Ruiz, Geometric theory of waves and its applications to plasma physics, Ph.D. Thesis, submitted to Department of Astrophysical Sciences, Princeton University (September, 2017).Advisor: I. Y. Dodin

Seth Davidovits, Understanding turbulence in compressing plasmas and its exploitation or prevention, Ph.D. Thesis, submitted to Department of Astrophysical Sciences, Princeton University (September, 2017).Advisor N. J. Fisch

Patent Applications1. Otto and diesel cycles employing spinning gas, US Patent Application 14/669,936; Filed March 26,

2015. Continued prosecution 2018. Inventors: V. I. Geyko and N. J. Fisch.Provisional Patent Applications1. Backward Raman Amplifier with Plasma Wave Seed, US Provisional Patent Application, 62/532,029;

Filed July 13, 2017. Inventors: K. Qu, I. Barth, and N. J. Fisch.2. Laser Pulse Compressor Using Magnetized Plasmas, US Provisional Patent Application, 62/578,836;

Filed October 30, 2017. Inventors: Y. Shi, N. J. Fisch, and H. Qin.

References October 2017 – March 2018

Fast Compression By RBS

b

T

pulse

Self-similar solutions:b ~ tT ~ 1/tE = b2T ~ tz ~ t

at caz V f b

ft Va b*

bt cbz Vaf *

V p / 2

aeApump

mec2 , b

eApulse

mec2 ,

f is normalized plasma wave amplitude

p

Resonant Raman Amplification and CompressionPump

a

plasma wave

p

c

ka b p

k a

k b

k p

resonancecondition

Self-similar “-pulse” regime

Malkin, Shvets, and Fisch (PRL, 1999)Goal:Focused intensity at 1 micron ~ 1025 W cm-2

Trmnrn

2exp)(

22

0

constT

In equilibrium

Cylinder with spinning particles compressed in axial direction

As temperature rises, particles are pushed towards to the center, making the periphery cooler and center hotter.

Geyko and Fisch (PRE, 2016)

Piezo-thermal Effect in Neutral Spinning Gases

This is exactly analogous to piezo-electric effect; heat flow takes the place of charge flow.

Ruiz et al, Phys. Plasmas (2016)

Simulations of the zonostrophic instability: improved and traditional WKEs.

Simulations show very different physics than that predictedby the traditional WKE (Diamond et al, 2005), whichignores full‐wave effects and total‐enstrophy conservation.

This NNSA‐sponsored research has stimulated a separateproject, which is presently sponsored by the DOE.

A quantumlike Moyal equation for the Wigner tensor of aturbulent field is proposed as an intuitive alternative to CE2:

Application: Full‐wave statistical modeling of inhomogeneous turbulence

Example: quasilinear model of drift turbulence + zonal flows

Wigner‐Moyal simulations from the follow‐up project funded by the DOE (Zhu et al, arXiv:1712.08262)

y

py

The turbulence is understood as an effective plasma:DW = quantumlike particles, ZF = collective field