MHD instability driven by fast electron streaming Tony Bell University of Oxford

1. MHD instability driven by fast electron streaming Tony Bell University of Oxford Rutherford Appleton Laboratory

2. Fast electrons in high intensity laser-plasma experiments behave like cosmic rays. In both cases, highly energetic charged particles with a large Larmor radius stream through a thermal plasma which behaves as an MHD fluid. Cosmic rays are confined close to the outer shock of supernova remnants by an amplified tangled magnetic field produced by an MHD instability driven by the cosmic rays. The same MHD instability may be driven by fast electrons in laser-plasma experiments relevant to Fast Ignition. At solid density the growth rate is of the order of 1 psec. At lower densities as in an ablated corona the instability grows more rapidly. The MHD instability grows more slowly than the Weibel instability, but it grows on a larger scale and may be more effective in inhibiting fast electron transport, especially for Fast Ignition laser pulses lasting ~10psec.

3. MHD instability due to cosmic rays Tycho 1572AD Kepler 1604AD Supernova remnants MHD instability produces magnetic field Driven by cosmic ray streaming Thin outer shock due to synchrotron cooling in large B SN1006 Cas A 1680AD

4. MHD instability due to laser-produced fast electrons High density plasma LASER High intensity (1019Wcm-2) Short pulse (psec) Fast (MeV) electrons B~1-100MG Units of 10MG Two instabilities driven by streaming fast electrons • Weibel instability • Grows rapidly on fsec timescale • Filaments currents on length scale c/wpe • No ion motion in simplest form • MHD instability • Grows on psec timescale • Starts small; grows non-linearly by spatial expansion • Ion motion an essential role

5. MHD instability driven by fast electrons Fast electrons Larmor radius > instability scalelength Detached from instability Uniform constant electric current Thermal electrons Larmor radius ~ instability scalelength Provide return current Frozen to field linea (approx) Fast e- current Magnetic field frozen into thermal plasma j j x B j B j x B Current carried by thermal plasma j x B force expands the spiral POSITIVE FEEDBACK (INSTABILITY)

6. Energetic particles coupled to MHD plasma Lucek & Bell (2000) applied to cosmic rays Demonstrated dB/B>>1

7. Non-linear growth 3D MHD with fixed fast electron current fast electron current Slices through |B| - time sequence Cavities and walls in |B| & r Non-linear growth: expending spirals/cavities Field lines: wandering spirals

8. Dispersion relation: linearise for parallel k, B & jfast Fluid acceleration Maxwell Ideal MHD Ohm’s law Growth rate Drift velocity of return current Growth limited by field tension at short wavelength Ion Larmor frequency

9. Growth rate (neglecting k2vA2) B in 100MG energy carried by fast electrons in 1019 Wcm-2 k in mm-1 density in gm cm-3 fast electron energy in MeV 100 10 Growth rate (psec-1) 1 0.1 0.01 0.1 1 10 100 wavenumber k (mm-1)

10. Comparison: equations for MHD & Weibel instabilities MHD Weibel Fast electron momentum a r a a Thermal electron momentum a r Thermal ion momentum Maxwell Essence of MHD instability: fast electrons are relatively unmagnetised thermal electrons are magnetised thermal ions provide inertia

11. Expanding spiral filament (1D cylindrical MHD) Magnetic field Bq Density Cavity in density and magnetic field

12. Natural evolution towards beam in cavity B E=0 R particle beam (imposed) E=-uxB E=0 Beam does work generating turbulence beam energy loss through electric field curl(E) produces B focuses particles, evacuates cavity Similar but different: fast electrons slowed by resistive electric field particles work against collisional resistivity GENERIC GENERATION OF MAG FIELD

13. Time sequence: magnitude of |B| - sections through beam Same results – integrated across beam