Intense Laser Matter Interactions & Electron Transport Issues

Transcription

1 Intense Laser Matter Interactions & Electron Transport Issues L. D. Van Woerkom Department of Physics The Ohio State University FSC Summer School July 2009 UCLA

2 Goals Introduction to Ultra-Intense Laser Matter Interactions A few issues in laser-driven electron transport

3 Motivation Basic physics of High Energy Density Science Laboratory Astrophysics Materials in extreme conditions Laser Driven Applications Fusion energy Ion beams Medical therapies Materials studies Electron beams Possible accelerator schemes Photon beams Bright x-ray and gamma sources for radiography

4 Inertial Confinement Fusion Laser energy Blowoff Inward transported thermal energy 1) Atmosphere formation: Laser beams rapidly heat the surface of the fusion target forming a surrounding plasma envelope. 2) Compression: Fuel is compressed by the rocket-like blowoff of the hot surface material. 3) Ignition: During the final part of the laser pulse, the fuel core reaches 20 times the density of lead and ignites at 100,000,000 degrees Celsius. 4) Burn: Thermonuclear burn spreads rapidly through the compressed fuel, yielding many times the input energy. Explosive burst Density ~ up to 1000 g/cc Confinement time ~10-10 s

5 Laser Driven Fusion

6 Big Picture Laser light -- electromagnetic disturbance Couples energy to charged particles This means electrons for most everything Energetic electrons Carry energy into/through material Lose energy to ions Lose energy to radiation Heated material then expands/explodes at long times Intense laser e - e -

7 The Story 1. High Intensity Lasers 2. Lasers & Single Electrons 3. Plasmas 4. Lasers & Plasmas 5. Transport 6. Maxwell s equations 7. Ion Acceleration 8. The end

8 Three Ways to Get Higher Intensity I = Energy AreaiTime Larger Energy Makes more electrons -- higher current Costly to build bigger lasers Shorter Pulse Same number of electrons Different dynamics due to shorter time Smaller Area Higher current density Limits due to diffraction and optical quality

9 Defining High Intensity Intensity Energy I = AreaiTime Define peak or average or. Pick an amount of energy Area containing this energy Time duration containing this energy Can be FWHM, 1/e, 40% of energy, etc. Be careful to be clear especially when comparing intensities How high is high? Typically these days in our field I W / cm Meaning of this soon..

10 Intensity Example I(x) x Total pulse energy = 120 J Assume 30% of energy between dashed x o = 10 μm Fluence = Energy/area = 0.3(120J)/(πx o2 ) = 1.1x10 7 J/cm 2 Assume pulse duration FWHM = 700 fs Peak intensity = 1.6x10 19 Wcm -2

11 Real Example Focusing Laser From Daniel Hey thesis Microscope + camera View actual focus at low power and map pixels by brightness into a circular gaussian beam

12 Typical Intense Lasers Get high intensity from lots of energy Lamp-pumped glass-type wavelength = 1 μm Energies from Joules Durations ~500 fs to 10 ps LLNL, LANL, MTW & LLE, Repetition rate several shots per day Get high intensity from shorter pulses Laser-pumped Ti:Sapphire wavelength = 0.8 μm Energies from Joules Durations ~ fs LLNL, Astra RAL, Universities Repetition rate several per day up to 1 shot per minute A little of each Mixed glass, 150 fs, 200 J Texas UT

13 Chirped Pulse Amplification

14 The Story 1. High Intensity Lasers 2. Lasers & Single Electrons 3. Plasmas 4. Lasers & Plasmas 5. Transport 6. Maxwell s equations 7. Ion Acceleration 8. The end

15 WIGGLING ELECTRONS - Ert (, ) = Eo ( rt, )cosωt F = ee( r, t) = ma KE U p ( r ) 2 2 e Eo ( r) 2 Up ( r) = ~ Iλ 2 4mω U p ~ few I ~ Wcm -2

16 Relativistic Wiggling As the electron s velocity increases due to E increasing Need B field Need relativistic equations Fields represented by a vector potential w/ amplitude a 0 vos eeo ao = = c mωc A E = B= A t a o = 1 I = Wcm -2 scales as (a o ) 2 dp v = e E+ B dt c p p= γmv γ = 1+ mc d 2 ( γ mc ) = e( v i E) dt 2

17 Relativistic Intensities Intensity rises electron moves faster relativistic y KE = ET E0 = ( γ 1) E F E F B = ee o ev = B c At Wcm -2 quiver energy is 13 MeV scaling as I 1/2 Electric field is 100 kv/nm or 180 a.u. field ionizes bound electrons with up to 4 kev binding energy Iλ γ = x 10 Wcm z 18 2 Trajectory has forward motion due to magnetic force in plane polarized beam

18 Ponderomotive Force Force on charged particles Gradient of intensity Average over an optical period to get a quasi-static force. Varies as the pulse envelope varies in time

19 Electrons Gain Lots of Energy U p 2 Iλ = 0.511Mev x10 ( W / cm ) μm Iλ ( W / cm ) μm a o U p (MeV) Recall at low intensity a o is just v/c

20 The Story 1. High Intensity Lasers 2. Lasers & Single Electrons 3. Plasmas 4. Lasers & Plasmas 5. Transport 6. Maxwell s equations 7. Ion Acceleration 8. The end

21 Plasmas Collection of free positive & negative charges Globally neutral but locally can separate charge Consists of light electrons & heavy ions Charge distribution adjusts to avoid bare charge separation Charge screening Debye length = distance over which charge is covered λ D λ D okt B e kt B e Te( ev) ne e 4 π ne e ne( cm ) ε = = For dilute plasmas (n e ~10 12 cm -3, T e ~ 1 ev): cm λ D ~ 7 μm Solid density plasmas (n e ~10 24 cm -3, T e ~ 10 ev): λ D ~ 0.02 nm

22 Plasma Oscillations Consider a uniform plasma & 1-D Number density n e Surface charge density σ=enδx Electric field E=σ/ε o Newton s law for a test particle, e δx E δ x= δx cosω t o 2 d δ x m = ee = 2 dt p 2 ene ε δ x o ω p 2 2 ne e 4π ne e = = = 5.64x10 n ( cm ) s mε m o e

23 Neutralization Time & Plasma Freq. Time Scales of Associated with Neutralization are Directly Related to The Plasma Frequency (and thus the Density) τ = 2π ω p p 4 1/2 e ω = n For dilute plasmas (n e ~10 18 cm -3 ): τ = sec (0.1psec) Solid density plasmas (n e ~10 24 cm -3 ): 16 τ = 10 sec (0.1 femtosec)

24 The Story 1. High Intensity Lasers 2. Lasers & Single Electrons 3. Plasmas 4. Lasers & Plasmas 5. Transport 6. Maxwell s equations 7. Ion Acceleration 8. The end

25 Plasma Frequency & Light Can also view the plasma frequency from Maxwell equation & conductivity point of view Drude model Time between collisions for electrons = τ Drude DC conductivity Apply to an AC field 2 ne e τ σ = m σω ( ) σ = 1 iωτ Gives complex dielectric function (index of refraction) 2 ω p εω ( ) = 1 i ω ω+ τ 2 2 ne e 4π ne e ω p = = = 5.64x10 n ( cm ) s mε m o e

26 Critical Density Complex index of refraction absorption or no propagation When driving frequency = plasma frequency Index becomes complex k-vector imaginary component no propagation inside Light is reflected Critical Density n c = density where ω=ω p For light w/ wavelength = 1 micron n c = cm mεω o L mω L nc = = 1.1x10 λ ( μm) cm 2 2 e 4π e Higher frequency (shorter λ) penetrates to higher density

27 The Action is at Critical Density Whatever the density profile, light will propagate up to n c Light couples to electrons most strongly at n c If intensity is high enough (relativistic) γn c For solid density above critical density Different laser interactions Question is always what is the density profile? n s n x n c

28 Want to stick with high density Lots of physics in underdense plasma region n < n c Want to concentrate on overdense region n > n c How do I know if I need to deal with underdense? It already exists before the laser pulse arrives It is created by the laser Stick with trying to interact with solid density Only consider density profile created by the laser Look at how far ions move

29 Long vs Short Pulses Long duration laser pulses ~ns (10-9 sec) Ions move/expand hydrodynamics important Lots of interactions w/ stuff less dense than solid Short duration laser pulses ~fs-ps ( s) Ions don t move much Laser interacts mostly w/ higher density stuff Use the sound speed to determine regime 1 1 * 2 * 2 1 B e 7 Z 2 [ e ] mi A ZkT cs = 3.1x10 T ( kev ) cm / s

30 Examples of Long vs Short Use pulse duration & speed of sound to get distance ions move while laser is present 1 * 2 1 [ ] 2 Z D( nm) csδt 0.3 Te( kev ) Δt( fs) A Use Al A=26, Z * ~7-9, T e ~100eV=0.1keV D(nm)~0.053Δt(fs) Long pulse Δt~1ns = 10 6 fs D~5.3x10 4 nm=53 microns Much longer than wavelength (~1 micron) need hydrodynamics Short pulse -- Δt~1ps= 10 3 fs D~53 nm Hydrodynamics much less important Shorter pulse 30 fs D~1.6 nm

31 Scale Length & Laser Interactions If D > λ Need to worry about hydro Need to worry about underdense interactions If D < λ Ignore hydro (for our purposes) Consider over dense interactions

32 Laser Interactions w/ solid density D 0 can use Fresnel equations from optics Absorption given by 1-R D ~> λ solve Helmholtz eqns Assume Drude type dielectric function Assume harmonic time dependence (use linear approx) D > λ and p-polarize light (E-field pokes into surface) Resonance absorption see regular LPI stuff D < λ & short pulses & high intensity laser gets to overdense region collisional heating (inverse Bremsstrahlung) inefficient collisionless heating begins

33 Collisionless Heating Vacuum (or Brunel: not-so-resonant, resonant) Heating Ignore B-field E-field accelerates electrons near surface Requires some p-component of light (E poking surface) E = 2E sinθ d L E d E L θ Electrons slammed into surface w/ v~v os sinθ

34 Anomalous Skin Effect Normal skin effect For skin depth distance l s = c/ω p Electrons wiggle in laser field & energy loss via collisions Electron mean free path (mfp) < skin depth Anomalous Skin Effect Electrons get hotter higher speed, longer mfp Now mfp > skin depth Electrons carry energy further into plasma

35 J x B Heating Very high intensities the v x B force becomes important Accelerates electrons along k-vector Accelerates electrons at twice laser frequency 2 Fz ( vos) (1 cos ωt) z JxB electrons E L k Brunel electrons

36 Faking Laser Interactions In order to facilitate transport modeling fake the laser Use empirical or phenomenological scaling For I up to ~ Wcm -2 Beg Scaling Distribution injected into material w/ k B T e ~ I 1/3 Usually a Boltzmann or Maxwell-Boltzmann E 1 kt n e B e n E 2 e e E kt OR take intensity distribution I(r,t) to get scaling Now let k B T e (or avg energy) = U p at each space-time point At higher Intensity use relativistic Maxwellian e r t r o 2 I(,) rt = Ie e τ o B e

37 Distribution Functions Temperature kt Beg 1 2 Iλ 3 = ( MeV ).215* 10 Wcm μm Temperature kt Wilks 2 Iλ ( MeV ) =.511* *10 Wcm μm Coupling α( IWcm [ ]) = 1.41*10 *( I) Maxwellian Jüttner f( E) = 2 E π ( kt ) 3 e E kt E ( ) = ( + 2 ) ( ) kt ( ) f E E mc E E mc e Unnormalized

38 Laser Interactions in the real world In a perfect world Laser interacts with solid density High current burst of electrons transports energy In the real world Energy before main pulse Main short pulse interacts with low density plasma NOT solid Big lasers don t focus perfectly Generation of electrons & subsequent transport messy Most diagnostics are time-integrated

39 Real Pulses

40 Real Beams

41 PrePlasma Top view probe Side view From Daniel Hey thesis Drive laser

42 The Story 1. High Intensity Lasers 2. Lasers & Single Electrons 3. Plasmas 4. Lasers & Plasmas 5. Transport 6. Maxwell s equations 7. Ion Acceleration 8. The end

43 Transport Issues All the preceding processes generate hot electrons Hotter than surrounding background electrons How do they propagate in high densities? laser Φ sc ~ MV 150 J ps Iλ 2 ~ 8x solid target e - γ γ e - γ γ e - ions B > 10 MG

44 Charge Separation Issues Start with neutral solid target Laser ionizes & creates hot electrons High speed electrons want to stream into solid BUT Hot electrons move away from positive ions Massive electric fields build up & stop electrons We know they stream into material HOW? Recall solid density contains lots of low energy electrons So called cold or background or plasma electrons These supply charge & current neutralization

45 Material Resistivity 1.E-05 1.E-06 1 g/cc Spitzer resistivity for high T collision dominated: η~t -3/2 Resistivity Ohm m 1.E-07 1.E-08 1.E-09 Au Al CD 1 g/cc D2 1 g/cc CD 10 g/cc D2 10 g/cc CD 100 g/cc D2 100 g/cc 10 g/cc 100 g/cc Temperature ev High T faster electrons & lower collision cross section

46 Hot vs Cold electrons Laser generated hot electrons ~ MeV energies Background cold electrons ~ temperature of material Hot electrons couple to material Lower energy hot electrons couple to material Temperature rises for cold electrons & resistivity changes j = en v en c Typical experiments mega-amperes of hot electrons h h h Low density but very high speed Can a net current flow?

47 Current Issues ALFVEN LIMT Confined current made up of fast moving charges Self consistent B field of current I Current I increases, the B-field intensifies, until electrons bent back upon themselves by v x B forces. In vacuum 17 βγka RETURN CURRENT Simple energetics require a return current 1 ps laser pulse focused to spot ~30 µm, absorbed intensity of W/cm 2 energy per pulse ~7J, (10 14 fast e bunch ~60 μm in length (RMS 200 kev fast e - range in Al); magnetic field on surface of cylinder ~3200 MG magnetic field energy of 5 kj! --A.Bell, et al., Plasma Phys Control Fusion (1997)

48 Return Current Must have return current to conserve energy Must have return current to cancel charge separation Net current in the material is ~0 j 0 = j + j j = n ev j = n ev net hot return hot hot hot return return return nhotvhot = nreturnvreturn v v n n hot return hot return Fundamental constraints for these arguments Hot electron density must be small

49 The Picture Large number of slow electrons are drawn in to neutralize the fast electrons Laser Ionization creates fast forward electron stream Hybrid PIC model ( Paris) L Gremillet G Bonnaud, F Amiranoff POP 9,941,(2002) If original hot electron current exceeds Alfven limit, filaments into many small components, each separated by return currents

50 But wait, there s more. Return current cold, slow moving electrons Coulomb cross section big Resistivity big much bigger than for hot electrons Cold electrons see high resistivitiy Set up electric field E=ηj This field slows down the hot electrons Known as Ohmic inhibition 1D model Plasma Phys. Control. Fusion 39 (1997) D effects like divergence of beam shorten distances

51 Ohmic Inhibition From King et. al; Phys. Plasmas 16, (2009)

52 The Story 1. High Intensity Lasers 2. Lasers & Single Electrons 3. Plasmas 4. Lasers & Plasmas 5. Transport 6. Maxwell s equations 7. Ion Acceleration 8. The end

53 What about the net current? Look to Maxwell B E = B = μ0jnet + μ0ε 0 t E driven by return current E = η j j j return return hot E t Ignore displacement current B E = ( η jreturn) = ( η jhot ) = η jhot η jhot = t Spatial variation in resistivity Spatial variation in hot electron current

54 The Picture, Again Spatial variation in j hot gives time varying B Curl of generated B net current BUT we assumed it was zero! Hybrid PIC model ( Paris) L Gremillet G Bonnaud, F Amiranoff POP 9,941,(2002)

55 Magnetic Fields vhot vcold jhot jcold j induced E ( ) y x Bz ( x) y j induced E ( ) y x Bz ( x) j induced ponderomotive thermoelectric Target surface n I e T n e Incident laser x Assume η uniform jhot jcold E = η jcold η jhot B E = t B E z y = t x B= μ j o induced

56 Gradient Induced Magnetic Fields thermoelectric T n e n c Field pinches expanding Plasma electrons T T n e ponderomotive n I e I n c I n e

57 Part of the Current Story Inside the beam hot electrons Current canceled by cold return current Net current very close to zero Edges of beam Time varying B-field due to spatially varying current Induced current forms net current on edges Other sources of magnetic fields Gradients in T & n Ponderomotive forces

58 The Story 1. High Intensity Lasers 2. Lasers & Single Electrons 3. Plasmas 4. Lasers & Plasmas 5. Transport 6. Maxwell s equations 7. Ion Acceleration 8. The end

59 Electrons Drive Ions Target Normal Sheath Acceleration Laser accelerates electrons Some leave, some reflux Very high fields produced at target surfaces and edges Atoms near and on the surface are ionized and accelerated by sheath fields Heavy ions see an averaged complex electron motion Smooth fields normal to the target surface Short Duration, ~ps Small Source, ~200 ~10 microns μm Smaller Virtual Source ~microns High Brightness / Low emittance E-field

60 Accelerating ions N ion N e, cold Electric Field (constant) ~ T hot /e l ion N e, hot + ++ Ion front N e,hot + N e, cold = N ion Ion charge sheet Debye Sheath where ion (local) Debye (local) REFLUXING REGION: V hot is max at ion charge sheet And is zero at ion front

61 Nice Proton Beams From P. Patel

62 Protons can be focused Measure visible light from heating as a function of time. SOP From P. Patel PRL

63 The Story 1. High Intensity Lasers 2. Lasers & Single Electrons 3. Plasmas 4. Lasers & Plasmas 5. Transport 6. Maxwell s equations 7. Ion Acceleration 8. The end

64 Conclusions Way too much information. Intense, short pulse lasers drive electrons relativistically Ponderomotive energy is a key figure of merit For short pulses, hydrodynamics sort of minimized Transport is complicated Current balance of hot and cold electrons important Net currents at the edges Hot electrons drive electric fields that accelerate ions Intense Laser Matter interactions coupled w/ Transport offers a rich environment for studying interesting science