1. Fast Ignition Fast Ignition: Some Issues in Electron Transport 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 Richard R. Freeman The Ohio State University

2. 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

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

4. MeV electron energy transfer (N c to 10 5 N c ) determines fast ignition threshold 1 100 10 4 Laser Electrons Anomalous Energy loss ? Shaping/collimating beam? n/n c “critical density” Fuel core density ~ 200

5. 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

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

8. 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

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

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

11. Time Scales of Associated with Neutralization are Directly Related to The Plasma Frequency (and thus the Density) For dilute plasmas (n e ~10 18 ): Solid density plasmas (n e ~10 24 ):

12. 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

13. There are two fundamental ideas that must be kept in mind when Large current flows, especially in high density materials 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 Confined current made up of fast moving charges Self consistent B field of current I RETURN CURRENT Laser pulse of 1 psec duration focused to a spot size of 30 µm, an absorbed laser intensity of 10 18 W/cm 2, corresponding to an energy per pulse of ~7J,(10 14 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), concomitant magnetic field energy of 5 kJ! 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) Simple energetics requires a return current

14. Laser Ionization creates fast forward electron stream Large number of slow electrons are drawn in to neutralize the fast electrons 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: ( j fast = n fast x v fast ) = ( j slow = n slow x v slow ) But v slow << v fast Thus, a new “limit” to keep in mind: n fast << n slow

15. 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

16. In working on experiments in current generation in solid materials from ionization by ultra-intense lasers—the reality is often very messy laser 1 kJ 0.5 ps I 2 ~ 3x10 20 + - - - - - - - + + + +   e-e- ions + e-e- e-e- solid target B > 10 MG  sc ~ MV    

17. In the relativistic regime the quiver energy of electrons in the laser EM field exceeds m e c 2 Relativistic quiver energy of a free electron is (  -1) m e c 2 where  =(1+I 2 /1.4x10 18 Wcm -2 ) 1/2 At 10 21 Wcm -2 quiver energy is 10 MeV scaling as I 1/2 Electric field is 100 kV/nm or 180 a.u. scaling as I 1/2 field ionizes bound electrons with up to 4 keV binding energy -ev  B/c -eE Trajectory has forward motion due to magnetic force in plane polarized beam

18. In the relativistic regime the quiver energy of electrons in the laser EM field exceeds m e c 2 Relativistic quiver energy E Q of a free electron is (  -1) m e c 2 where  =(1+I 2 /1.4x10 18 Wcm -2 ) 1/2

19. 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

20. Modeling is now done with “Ideal” Laser Pulses

21. Modeling is now done with “Ideal” Laser Pulses

22. A “REAL” interaction environment

23. Target : 50  m CH E ~ 600J  p = 5ps; I ~ 5x10 19 Wcm -2 Original target surface Ever-present prepulse creates plasma on front of target, here measured by interferometry.

24. 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

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

26. Refluxing electrons dominate the target

27. 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 4 th power of the relative velocity. For fast enough electrons, they simply don’t “see” the material 1.E- 09 1.E-08 1.E-07 1.E-06 1.E-05 0.11101001000 Temperature eV Resistivity Ohm m Current expts DT fuel Au cone ?? Ohmic limit in FI CD 1 g/cc D2 10 g/cc 100 g/cc AuAu CDCD 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 Remember the RETURN CURRENT? This is where the material’s resistivity enters the problem

28. 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

29. Experimental Studies of Laser Generated Electrons: Method

30. First results of side-imaging of currents

31. Al/Cu alloy K  image -showing spreading at entry surface and rapid axial attenuation 6 beam 1 500 µm Horizontal (axial) Vertical (radial) 90  m 32  m

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

33. 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

34. 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? in Al is as much as a millimeter?

35. 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 4. potential Maximum Fast electron Kinetic energy d Potential stops fast electrons in much Shorter distance than collisions. Effect Depends upon resistivity of material and Number of fast electrons

40. Extra Material (if time) Experiments where N fast > N background

41. S.B - 7th FIW - 04/2004- 8 Gas jet experiment : study of a new regime of electron transport (n fast > n background )  = 350 fs 1,057 µm E = 5 J  = 528 n m = 350 fs 1 0.1 J mm  - Gas Jet (He, Ar) P = 30, 50, 70, 80 bar Interaction beamProbe beam E 0.0 16  = = Other diagnostics (X, OTR) Time resolved shadowgraphy The delay between the CPA and the probe beam is changed from shot to shot

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

43. S.B - 7th FIW - 04/2004- 10 Expansion of electron cloud obtained by shadowgraphy time-series Gas jet: Ar 70 bar Gas atomic density: 2.7 x 10 19 cm -3 Laser intensity: 3 - 4 10 19 W/cm 2 By changing the delay between the CPA beam and the probe beam we can reconstruct the evolution of the electron cloud CPA beam t 0 t 0 + 4 ps t 0 + 13 ps

44. minimal size of electronic cloud    m v cloud  c/30  c/10 v cloud increases with plasma density v jets  c/2 at least Electron cloud velocity increases with plasma density S.B - 7th FIW - 04/2004- 11 He 30 : 2 10 19 cm -3 He 80 : 6 10 19 cm - 3 Ar 30 : 7 10 19 cm -3 Ar 70 : 2 10 20 cm -3