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

Department of Astrophysical Sciences, Princeton UniversityGoals1. Identify methods for next generation light intensities

2. Identify new effects in highly compressed plasma

3. Formulate general description of fundamental wave effects

Supported in 2019: Y. Shi. E. Kolmes and V. Munirov (graduate students); Q. Jia and K. Qu (postdocs); and V. M. Malkin (research staff)

Collaborators: Professor J. Mikhailova (Princeton), Dr. I. Barth (Hebrew U.)M. Edwards (graduate student, advisor J. Mikhailova)

Recent graduates involved in our NNSA sponsored research: Z. Toroker *15 (Intel) M. Hay *16 (Volant) V. Geyko *17 (LLNL)D. Ruiz *17 (SNL) S. Davidovits *17 (LLNL) Y. Shi *18 (LLNL) M. Edwards *19 (LLNL)

2018 Stewardship Science Academic Programs Symposium, Washington, DC, February 26, 2020

This talk will cover: 1. Underlying motivation2. Some recent work3. Mainly present directions

Archival Publications: October 2018 to September 2019

K. Qu and N. J. Fisch, Creating localized plasma wave by ionization of doped semiconductors,Physical Review E 99, 063201 (June, 2019).

M. R. Edwards, Y. Shi, J. M. Mikhailova, and N. J. Fisch, Laser Amplification in Strongly-Magnetized Plasma, Physical Review Letters 123, 025001(July, 2019).

R. Gueroult, Y. Shi, J. M. Rax, and N. J. Fisch, Determining the rotation direction in pulsars, Nature Communications 10, 3232 (July, 2019).

K. Qu and N. J. Fisch. Laser frequency upconversion in plasmas with finite ionization rates,Physics of Plasmas 26, 083105 (August, 2019).

V. M. Munirov and N. J. Fisch, Radiation in equilibrium with plasma and plasma effects on cosmic microwave background,Physical Review E 100, 023202 (August, 2019).

V. Geyko *17 (LLNL)D. Ruiz *17 (SNL) S. Davidovits *17 (LLNL) Y. Shi *18 (LLNL), Plasma Physics in Strong Field Regimes (co-advisor H. Qin)M. R. Edwards *19 (LLNL) Ultrafast Sources of Intense Radiation (advisor J. Mikhailova)

Recent Ph.D. Dissertations acknowledging support from NNSA

Patents acknowledging support from NNSA

V. I Geyko and N. J. Fisch, Otto and Diesel Cycles Employing Spinning Gas, US patent Application 14/669,936, Filed March 26, 2015US Patent No. 10,450,943, issued October 22, 2019. (spin-off application of physics of compressing a rotating plasma)

Peer Reviewed Conference Proceedings (2019)

I. Barth and N. J. Fisch, Spectral Manipulation of Raman Amplifiers, Proceedings of the 27th Annual International Laser Physics Workshop (LPHYS’18), Journal of Physics: Conf. Series 1206, 012015 (2019).

K. Qu and N. J. Fisch, Plasma optics for intense laser amplification, Proceedings of SPIE 11036, Relativistic Plasma Waves and Particle Beams as Coherent and Incoherent Radiation Sources III, 1103602 (April, 2019).

Major Goals in Next Generation Light Sources

1. Highest intensity light beyond chirped pulse amplificationa. at optical wavelengthsb. at shorter wavelengths (no CPA competition)

2. Highest power light at ever shorter wavelengthsa. Megajoules available at optical wavelengthsb. Efficient upconversion to shorter wavelengths

Solutions lie through mediation of light in plasma

How can light be compressed in time in plasma?

Goal: Reach laser intensities higher than possible using material optical elements

CPA techniques are limited by material properties

Limitation in intensity at grating ~ TW/cm2 at 1µLimitation in fluence ~ J/cm2 at 1µ and 1-10 ps

But plasma is not so limited (nonrelativistic at TW/cm2 at 1µ)

Resonant Raman Amplification and Compressionpump a

plasma wavepω

c

ω

kresonancecondition

Self-similar “π-pulse” regime

Malkin, Shvets, and Fisch (PRL, 1999)

Goal:focused intensity at 1 micron ~ 1025 Wcm-2

seed b

Creating plasma waves by ionizing doped semiconductors• Ionize periodically aligned p-n junction semiconductors.

• Differential doping creates electrostatic fields 𝐸𝐸 ~100 kV/cm.

• Upon ionization, the E-fields initiate plasma waves.

• Get quasi-homogeneous ion density. Issues in collisional damping and dissipation in ionization.

Qu & Fisch, PRE 99, 063201 (2019)

plasmawavepω

ω

k

pump

Chirped Photon Acceleration

Energy distribution after flash ionization

Flash ionization upshifts frequenciesIn gradient, produce chirped pulse, allowing recompression.

Edwards, Qu, Jia, Mikhailova, and Fisch, Phys. Plasmas (2018).Qu, Jia, Edwards, and Fisch, Physical Review E (2018).Qu and Fisch, Physics of Plasmas (2019).

High-efficiency, resonant frequency-doubling in very under-critical plasma

V. M. Malkin and N. J. Fisch, arXiv:1909.01453v1 (2019); Phys. Rev. E 101, 023211 (2020) Towards Megajoule X-ray Lasers via Relativistic 4-Photon Cascade in Plasma

k1 k2

k3 k4

zparaxial beams

MJ in optical MJ in x-ray in 10 frequency doublingsMJ in optical kJ in x-ray at 50% efficiency in each stage

Frequency Doubling via 4-wave interaction in very under-critical plasma

Decouples plasma amplification from plasma resonance1. Insensitive to plasma inhomogeneities2. Low plasma density delays filamentation instability of output pulse3. Automatic resonance — since (4) is generated and lost, carrying entropy4. Near doubling of frequency5. Many possible resonances

Pump pulses (1) and (2) amplified pulse (3) and a disposable laser pulse (4).

k1 k2

k3 k4

In principle, high efficiency, reasonable growth distance

Linear growth rate

For 𝑎𝑎1=0.1, 𝑘𝑘1⊥=𝑘𝑘1/7, ω4=ω1/5, ωp=ω1/50, 𝜆𝜆1=350 nm

𝑐𝑐/𝛾𝛾 ≈ 30 cm

For 𝑘𝑘1 ≈ 𝑘𝑘2 and 𝑘𝑘4 ≪ 𝑘𝑘3, nearly all energy flows to pulse 4

𝑎𝑎 = v/c

Waveguide implementation (reflection at grazing angles)

60 cm amplification enables 2 exponentiations in amplitude, or 4 exponentiations in intensity

𝑃𝑃𝑐𝑐𝑐𝑐 = 4.25 TW R = 2ω1𝜆𝜆1/π𝑎𝑎1ωe ≈ 0.08 mm2 pump implementation: P = 2𝑃𝑃𝑐𝑐𝑐𝑐 = 8.5 TW

𝑎𝑎1=0.1, 𝑘𝑘1⊥=𝑘𝑘1/7, ω4=ω1/5, ωp=ω1/50, 𝜆𝜆1=350 nm

in over-moded cylindrical channelazimuthal wavenumbers perpendicular

ground state radial mode

8 pump beams

Avoiding Transverse Filamentation Instability at Overcritical Powers

Solution: Use multiple weakly-coupled pumps with each below the critical power

k1 k2

k3 k4

k1 k2

k3 k4

Coupling is weak enough if all sub-pumps are separated by δω and δ𝑘𝑘⊥ satisfying

(δω/ωp - 1) δ𝑘𝑘⊥2𝑐𝑐2/ω𝑝𝑝

2 ≫ 𝑎𝑎12

which is a mild condition accommodating many pump pulses

Opportunities in higher order nonlinear laser interactions• Mildly relativistic intense laser pulses, with quiver electron velocity 𝑣𝑣

small, can be expanded in powers of 𝑎𝑎 = 𝑣𝑣/𝑐𝑐 ≪ 1.

• For large laser power below the critical power of relativistic self-focusing, 𝑃𝑃𝑐𝑐𝑐𝑐 = 𝑚𝑚2𝑐𝑐5ω2/𝑒𝑒2ω𝑒𝑒

2 ≈ 17ω2/ω𝑒𝑒2 GW, require ω/ωe ≫ 1.

• Regimes with ω𝑒𝑒/ω ≪ 𝑎𝑎 ≪ 1 are of interest, with rates of nonlinear N-wave interactions ~ 𝑎𝑎𝑁𝑁−2.

• Finding the dominant interaction at mildly small 𝑎𝑎 is complicated by presence of other small parameters.

• 6-photon interactions hold particular promise for frequency tripling.

Preliminary Studies: Optimizing Focal Spot for 4-wave Seed Amplification

Over-focusing:Large dump beam dispersionShort pump-seed overlap=> Wide and low energy amplified seed

Moderate-focusing: w0 = 12Less dump beam dispersionDepleted pumps

⇒Higher intensity amplified seed⇒20% of total pump energy captured

Under-focusing: Lower intensity pumpsweaker nonlinear interaction=> Energy left on the table for seed

A. Griffith et al (2020)

seed

pump

pump

disposable

Solve coupled-mode equationsView in seed frame

t = 0 t = 200 t = 400

Preliminary PIC Simulations: Filamentation seeds Forward Raman Scattering

,

ky K. Lezhnin et al.

transverse filamentation&FRS pulses

laser pulseI=3e16 W/cm2, 100 fsmicron wavelength

uniform underdense plasmane/ncr=0.2

t Kinetic simulations show simultaneous appearance of FRS, BRS & filamentation (Decker et al., Phys. Rev. E, 1994; Coverdale et al., Phys. Rev. Lett., 1995; Trines et al., Nat. Phys. 2010)

QED laser intensity with Colliding e-Beams

𝑒𝑒− beam

1𝑛𝑛𝑛𝑛30𝐺𝐺𝑒𝑒𝐺𝐺

3 𝑃𝑃𝑃𝑃1022𝑃𝑃/𝑐𝑐𝑚𝑚2

𝑎𝑎 ≈ 70𝜒𝜒~25

S. Meuren, et al, On Seminal HEDP Research Opportunities Enabled by Co-locatingMulti-Petawatt Laser with High-Density Electron Beams, arXiv:2002.1005 (2020).

Schwinger limit (𝐸𝐸𝑐𝑐𝑐𝑐~1.3 × 1018 𝐺𝐺/𝑚𝑚) for 𝑒𝑒−- 𝑒𝑒+ creation in vacuum.

Reach 𝐸𝐸𝑐𝑐𝑐𝑐 with state-of-the-art lasers in rest frame, with 𝐸𝐸∗ → 𝛾𝛾𝐸𝐸 > 𝐸𝐸𝑐𝑐𝑐𝑐, when colliding with an energetic 𝑒𝑒− beam.

When 𝜒𝜒 = 𝐸𝐸∗/𝐸𝐸𝑐𝑐𝑐𝑐 ≫ 1, the QED cascade can create a pair plasma

Each 𝑒𝑒− can create ~ 𝜒𝜒 = 25 pairs. Pair energy decreases to 𝛾𝛾~100 via synchrotron radiation.

Difficulties in observing collective effects of pair plasmas

• High pair energy (𝛾𝛾 > 100) ⟶ increased particle mass ⟶ low plasma frequency

• High velocity (~𝑐𝑐) ⟶ difficult to detect plasma evolution while tracking

• Small dimension (𝐿𝐿~𝜇𝜇m) • The pair size 𝐿𝐿 < 𝜆𝜆𝐷𝐷 (Debye length) ⟶ not quasi-neutral• The pair size 𝐿𝐿 < 𝑙𝑙𝑠𝑠 (skin depth) for typical lasers/RF waves ⟶ no reflection• The cut-off wavelength 𝜆𝜆co > a few hundred 𝜇𝜇𝑚𝑚

Signature of collective plasma effects: laser frequency upshift

𝜔𝜔0 = 𝑐𝑐𝑘𝑘 → 𝜔𝜔 = 𝜔𝜔𝑝𝑝2/𝛾𝛾 + 𝑐𝑐2𝑘𝑘2

𝜔𝜔𝑝𝑝2/𝛾𝛾

𝑘𝑘

𝜔𝜔

K. Qu, S. Meuren, & N. J. Fisch, Observing Collective Plasma Effects in Beam-Driven QED Cascades via Laser Frequency Upconversion, arXiv:2001.02590 (2020).

Pair plasmas generated inside laser field.

Laser frequency increases with pair increase or with pair energy decrease

3 Signatures in laser spectrum

Laser envelope

Radiation envelope

Propagation [𝜇𝜇m]

Tran

sver

se [𝜇𝜇

m]]

Wavelength [𝜇𝜇m]

Laser chirping

Propagation [𝜇𝜇m]

Tran

sver

se [𝜇𝜇

m]

Tran

sver

se [𝜇𝜇

m]input laser peak

output laser peak

1. Blue shift

2. Diffraction

3. Frequency Chirp

Frequency upshift --- QED-PIC simulations

Frequency upshift linearly increases with 𝑒𝑒− beam density and 𝑒𝑒− beam energy:

Frequency upshift is, however, not sensitive to laser intensity:Pa

ir de

nsity

Pair

ener

gySi

mul

ated

freq

upsh

ift

Pred

icte

dfr

equp

shift

PIC simulation

• Gaussian Laser: 0.8𝜇𝜇𝑚𝑚, 50fs ×(5μm) 2, 6 × 1022 W/cm2, 𝑎𝑎 ≈ 160• 𝑒𝑒− beam: 300GeV, 1nC (Gaussian distribution 1μm3, 4 × 1020 cm-3)

• Created pair plasma: ~3.2 × 1022 cm-3, 𝛾𝛾 ≈ 100• Laser spectrum: ∆𝜔𝜔𝑐𝑐𝑒𝑒𝑐𝑐𝑐𝑐𝑒𝑒𝑐𝑐/𝜔𝜔0 ≈0.2%, ∆𝜔𝜔𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑝𝑝𝑒𝑒𝑐𝑐,𝑚𝑚𝑚𝑚𝑚𝑚/𝜔𝜔0 ≈3%.

Summary1. Goal: Highest intensity light beyond chirped pulse amplification

a. Could initiate Raman compression with plasma waveb. Suggestion: ionize p-n junction to produce plasma wave (dissipative)

2. Goal: Upshift optical light at high power a. Ionization upshift and stretching cascade – (dissipative)b. Resonant 4-wave: in principle highly efficient

3. Goal: 4-photon plasma-mediated upconversion – optical to x-raya. Use density just for coupling insensitive to inhomogeneityb. Solve critical power by multiple resonancesc. Carry off entropy in disposable pulse 4 d. Get MJ optical to MJ x-ray in 10 stages (or kJ at 50% efficiency)!

4. Goal– Identify signatures of pair plasmaa. Upshift optical light, identify features in frequency chirp and radiation patternb. Suggests opportunity in co-locating laser and beam sources!