Fast Ignition : Some Issues in Electron Transport

Fast Ignition:Some Issues in Electron Transport Richard R. Freeman The Ohio State University Some fundamentals of large currents moving through dense materials Some unexpected problems the community has faced and understood Some more unexpected problems that are under intense study

Elements of 2 lectures of Electron Transport in Fast Ignition • Context of electron transport in FI • Concepts of time scales within a plasma • The role of Alfven and “return” currents • Overview of electrons in extreme laser fields • The “real” environment in experiment vs. “ideal” • Sheath fields and refluxing • Example #1 of Experimental Surprise: • Low energy electrons spreading at front surface • Example #2 of Experimental Surprise: - Short penetration depth of fast electrons

“Under-dense” Corona surrounding core “over-dense” Corona surrounding core Relativistic “critical density”

104 100 1 MeV electron energy transfer (Nc to 105 Nc) determines fast ignition threshold Fuel core density n/nc “critical density” ~ 200 Anomalous Energy loss ? Shaping/collimating beam? Electrons Laser

Laser gets to this point either Through non linear effects or cone Laser converts E&M energy to fast Electrons with ~30% efficiency Fast electron beam must stay Collimated to deliver its energy

But the target is neutral when the ultra-intense laser hits it; • the current comes from ionization; • the material remains neutral; • What are the Dynamics under these Conditions?

Richard Fitzpatrick http://farside.ph.utexas.edu/ Teaching/plasma/lectures/ Node6.html

Time Scales of Associated with Neutralization are Directly Related to The Plasma Frequency (and thus the Density) For dilute plasmas (ne~1018): Solid density plasmas (ne ~1024):

There are two fundamental ideas that must be kept in mind when Large current flows, especially in high density materials Self consistent B field of current I Confined current made up of fast moving charges ALFVEN LIMT As the current I increases, the B field intensifies, until individual electrons Are bent back upon them selves by V X B forces. This value, in a vacuum, Is 17 kA RETURN CURRENT Simple energetics requires a return current Laser pulse of 1 psec duration focused to a spot size of 30 µm, an absorbed laser intensity of 1018 W/cm2, corresponding to an energy per pulse of ~7J,(1014 fast electrons @200keV). Take the bunch to be ~60 μm in length (corresponding to the RMS 200 keV fast electron range in AL) and a diameter of the laser spot size (30 μm), the magnetic field on the surface of the cylinder would be 3200 MG, with a concomitant magnetic field energy of 5 kJ!--A.Bell, et al., Plasma Phys Control Fusion 39 653 (1997)

Large number of slow electrons are drawn in to neutralize the fast electrons Laser Ionization creates fast forward electron stream The original fast electron beam, if it exceeds the Alfven limit, filaments into many small components, each separated by return currents What must exist, at times scales ~10-16 sec, everywhere in the material: ( jfast = nfast x vfast ) = ( jslow = nslow x vslow ) But vslow << vfast Thus, a new “limit” to keep in mind: nfast << nslow

In working on experiments in current generation in solid materials from ionization by ultra-intense lasers—the reality is often very messy Fsc ~ MV g solid target e- e- 1 kJ 0.5 ps Il2 ~ 3x1020 ions - ´ g + laser - + - - + + + - + · - g - e- g B > 10 MG

In the relativistic regime the quiver energy of electrons in the laser EM field exceeds mec2 • Relativistic quiver energy of a free electron is (g-1) mec2 where g=(1+Il2/1.4x1018Wcm-2)1/2 -evB/c Trajectory has forward motion due to magnetic force in plane polarized beam -eE • At 1021 Wcm-2 quiver energy is 10 MeV scaling as I1/2 • Electric field is 100 kV/nm or 180 a.u. scaling as I1/2 • field ionizes bound electrons • with up to 4 keV binding energy

In the relativistic regime the quiver energy of electrons in the laser EM field exceeds mec2 • Relativistic quiver energy EQ of a free electron is (g-1) mec2 where g=(1+Il2/1.4x1018Wcm-2)1/2

Modeling is now done with “Ideal” Laser Pulses

A “REAL” interaction environment

Ever-present prepulse creates plasma on front of target, here measured by interferometry. O r i g i n a l t a r g e t s u r f a c e T a r g e t : 5 0 m C H m E ~ 6 0 0 J 1 9 - 2 = 5 p s ; ~ 5 x 1 0 W c m I t p

A Schematic of how Sheath Fields are set up due to Target Neutrality: Acceleration Mechanism for Protons N ion Electric Field (constant) ~ Thot/e lion N e, cold N e, hot Ion front + + + Debye Sheath Ne,hot + Ne, cold = Nion where (local) ≤ (local) l l ion Debye Ion charge sheet REFLUXING REGION: Vhot is max at ion charge sheet And is zero at ion front

Refluxing electrons dominate the target

1.E-05 Current expts 1.E-06 CD 1 g/cc D2 Au cone ?? CD 1.E-07 Au Resistivity Ohm m Ohmic limit in FI 10 g/cc DT fuel 1.E-08 100 g/cc 1.E-09 0.1 1 10 100 1000 Temperature eV So why can fast electrons (>MeV) “reflux” in thin targets without immediately colliding with the ions of the material and stopping, or at least lose energy quickly? Remember your Jackson E&M? The Coulomb cross-section for charged particles drops at the 4th power of the relative velocity. For fast enough electrons, they simply don’t “see” the material Remember the RETURN CURRENT? This is where the material’s resistivity enters the problem So-called “Spitzer” regime: hotter material has lower resistivity. The fast electrons do not feel the materials resistivity, but the return current does, and this is the rub

Experimental Studies of Laser Generated Electrons: Method

First results of side-imaging of currents

Al/Cu alloy Ka image -showing spreading at entry surface and rapid axial attenuation • 6 beam 1 32 mm Horizontal (axial) Vertical (radial) 90 mm 500 µm

B ~1/r B ~ Ez E X B Blow-off Typical computed electron trajectory Hot electron source Region (critical) Variable density solid Return current Cf: Forslund and Brackbill PRL 48 1614 (82) J. Wallace, PRL 55 707 (85) B Z ro r

Problem: How can this transport distance be so short when the stopping distance of a few MeV electron in Al is as much as a millimeter?

Here’s where the “Return Current” and the material properties raise their heads 1. Fast forward current feels not material resistance 2. Electric Field is set up by neutrality condition to drive return current 3. Return Current, made up of vast numbers of slowly moving electrons. These electrons feel the resitivity of the material and through ohmic processes heat the material and setup a potential within the material. This potential acts to slow and stop the fast electrons in a much shorter distance than Coulomb collisions would predict Potential stops fast electrons in much Shorter distance than collisions. Effect Depends upon resistivity of material and Number of fast electrons Maximum Fast electron Kinetic energy 4. potential d

Extra Material (if time) • Experiments where Nfast > Nbackground

Other diagnostics (X, OTR) Interaction beam Probe beam = 3 5 0 f s = m 5 2 8 n t l 3 5 0 f s = l = 1,057 µm t = - E = 5 J 0 . 1 J 0 . 0 1 E = 1 6 m m Gas Jet ( H e , A r ) P = 3 0 , 5 0 , 7 0 , 8 0 b a r Gas jet experiment : study of a new regime of electron transport (nfast > nbackground) Time resolved shadowgraphy The delay between the CPA and the probe beam is changed from shot to shot S.B - 7th FIW - 04/2004- 8

Fused silica jets 400µm Vacuum Gas jet experiment : propagation in transparent media direct observation of electron jets and cloud Al (15m) Dt = 20 ps Gas jet (Ar 70 bar) Ti (20m) 1080 m jets CPA beam Gremillet et al. PRL 1999 Borghesi et al. PRL 1999 at 1.2 mm from nozzle Electronic jets moving at  c Extended electronic cloud moving at  c/2 S.B - 7th FIW - 04/2004- 9

Expansion of electron cloud obtained by shadowgraphy time-series Gas jet: Ar 70 bar Gas atomic density: 2.7 x 1019cm-3 Laser intensity: 3 - 4 1019 W/cm2 CPA beam t0 t0 + 4 ps t0 + 13 ps By changing the delay between the CPA beam and the probe beam we can reconstruct the evolution of the electron cloud S.B - 7th FIW - 04/2004- 10

Electron cloud velocity increases with plasma density He 30 : 2 1019 cm-3 He 80 : 6 1019 cm-3 Ar 30 : 7 1019 cm-3 Ar 70 : 2 1020 cm-3 • minimal size of electronic cloud   m • vcloud  c/30  c/10 • vcloud increases with plasma density • vjets  c/2 at least S.B - 7th FIW - 04/2004- 11

Fast Ignition : Some Issues in Electron Transport