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Collisionless Shocks

Collisionless Shocks. Manfred Scholer. Max-Planck-Institut für extraterrestrische Physik Garching, Germany. The Solar/Space MHD International Summer School 2011 USTC, Hefei, China, 2011.

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Collisionless Shocks

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  1. Collisionless Shocks Manfred Scholer Max-Planck-Institut für extraterrestrische Physik Garching, Germany The Solar/Space MHD International Summer School 2011 USTC, Hefei, China, 2011

  2. Tom Gold, 1953: Solar flare plasma injection creates a thin collisionless shock

  3. Criticality Above first critical Mach number resistivity (by whatever mechanism, e.g. ion sound anomalous resistivity) cannot provide all the dissipation required by the Rankine-Hugoniot conditions. Conclusion: additional dissipation needed. Question: what is this additional dissipation?

  4. Critical Mach Number (Leroy, Phys. Fluids 1983) 2-Fluid (one-dimensional) resistive MHD equations: Momentum equation for ions, momentum equation for massless electrons, energy equation for electrons Solve electron momentum equation for the electric field and insert into ion momentum equation Use Maxwells equation for curl B to substitute ion velocity for the electron velocity Integrate ion momentum equation to obtain ion velocity as function of magnetic field and electron pressure

  5. Critical Mach Number -II Assume that ions remain cold through the shock and eletrons are heated by Ohmic friction Obtain from the integrated momentum equation an equation for the x derivative of the electron pressure Insert this derivative into the energy equation of the electrons and obtain an equation for dv/dx This equation exhibits a singularity at the critical Mach number

  6. Low beta, almost perpendicular Edmiston & Kennel et al. 1984

  7. Oblique Shocks: Quasi-Parallel and Quasi-Perpendicular Shocks Shock normal angle QBn Trajectories of specularly reflected ions Important Parameters: Mach number MA Ion/electron beta

  8. This is why 45 degrees between shock normal and magnetic field is the dividing line between quasi-parallel and quasi-perpendicular shocks

  9. The Whistler Critical Mach number

  10. Quasi-perpendicular bow shock ion inertial length km Magneticfielddata in shock normal coordinates versus distancefromtheshock in km Horbury et al., 2001

  11. Magnetic Field the Quasi-Parallel Bow Shock Greenstadt et al., 1993

  12. Cluster measurements of large amplitude Pulsations (also called SLAMSs) Lucek et al. 2008

  13. Classification of Computer Simulation Models of Plasmas Kinetic Description Fluid Description Full particle codes PIC Vlasov Codes Hybrid Code MHD Codes Vlasov hybrid code Two-fluid code

  14. Simulation Methods 1. Hybrid Method Ions are (macro) particles Electrons are represented as a charge-neutralizing fluid Electric field is determined from the momentum equation of the electron fluid Assume massless electrons and solve for electric field is determined from the electrical current via where is the bulk velocity of the ions

  15. Simulation Methods 2. Particle-In-Cell (PIC) Method Both species, ions and electrons, are represented as particles Poisson‘s equation has to be solved Spatial and temporal scales of the electrons (gyration, Debye length) have to be resolved Disadventage: Needs huge computational resources Adventage: Gives information about processes on electron scales Describes self-consistently electron heating and acceleration

  16. Hybrid Simulation of 1-D or 2-D Planar Quasi-Parallel Collisionless Shocks Inject a thermal distribution from the left hand side of a numerical box Let these ions reflect at the right hand side The (collective) interaction of the incident and reflected ions results eventually in a shock which travels to the left Ion phase space vx - x (velocity in units of Mach number) Diffuse ions Transverse magnetic field component Large amplitude waves dB/B ~ 1

  17. Quasi-Perpendicular Collisionless Shocks • 1. Specular reflection of ions • 2. Size of foot • 3. Downstream exciation of the ion cyclotron instability • 4. Electron heating

  18. Schematic of a quasi-perpendicular supercritical shock

  19. Shock Upstream Downstream Esw B B Schematic of Ion Reflection and Downstream Thermalization vsw Core Foot Ramp

  20. Specular reflection in HT frame: guiding center motion is directed into downstream About 30% of incoming solar wind is specularly reflected

  21. Specularly reflected ions in the foot of the quasi-perpendicular bow shock – in situ observations Sckopke et al. 1983 Sun Specularly reflected ions Solar wind Ion velocity space distributions for an inbound bow shock crossing. Phase space density is shown in the ecliptic plane with sunward flow to the left. Sckopke et al. 1983

  22. Size of the foot

  23. Reflection of particles and upstreamacceleration leads to increase of the kinetic temperature. Is this the downstream thermalization? No! Process is time reversible. For dissipation we must have an irreversible process; entropy must increase! Scatter the resulting distribution!

  24. Yong Liu et al. 2005 Downstream Thermalization and Wave Excitation (Low Alfven Mach Number Case) Predicted magnetic field fluctuation power spectra obtained from the resonance condition Scattering leads to wave generation and to a bi-spherical distribution

  25. Downstream thermalization : Alfven ion cyclotron instability Winske and Quest 1988 Oblique propagating Alfven Ion Cyclotron waves produced by the perpendicular/parallel temperature anisotropy (Davidson & Ogden, Phys. Fluids, 1975)

  26. Situation in the foot region of a perpendicular shock B Ion and electron distributions in the foot Ions: unmagnetized Electrons: magnetized

  27. Possible microinstabilities in the foot Wave type Necessary condition Buneman inst. Upper hybrid Du >> vte (Langmuir) Ion acoustic inst. Ion acoustic Te >> Ti Bernstein inst. Cyclotron harmonics Du > vte Modified two-stream inst. Oblique whistler Du/cosq > vte

  28. Instabilities in the Foot and Shock Re-Formation Instability between incoming ions and incoming electrons leads to perpendicular ion trapping Reflected ions not effected

  29. Burgess 2006 Shock Ripples Electron acceleration (test particle electrons in hybrid code shock) Ripples are surface waves on shock front Move along shock surface with Alfven velocity given by magnetic field in overshoot Shocks with no ripples Shock with ripples

  30. ElectronHeating Electron heating at heliospheric shocks is small. Ratio of downstream to upstream temperature about 3 - 4. Downstream temperature usually amounts to an average of about 12% of the upstream flow energy (for a wide range of shock parameters, Including Mach number). Laboratory shock studied in the 70s had downstream to upstream electron temperature ratios of up to 70! Macrosacopic scales larger than electron gyroradius – electrons are magnetized whereas ions are de- or only partially magnetized Decoupling of ions and electrons at the shock and different thermalization histories

  31. Electron distributiuon function through the shock Feldman et al. 1982

  32. Cross-shock potential and electron heating Offset peak produced by shock potential drop in the HT frame Filled in by scattering

  33. Quasi-Parallel Collisionless Shocks Parker (1961): Collisionless parallel shock is due to firehose instability when upstream plasma penetrates into downstream plasma Golden et al. (1973) Group standing ion cyclotron mode excited by interpenetrating beam produces turbulence of parallel shock waves Early papers did not recognize importance of backstreaming ions • 1. Excitation of upsteam waves and downstream convection • 2. Upstream vs downstream directed group velocity • 3. Mode conversion of waves at shock • 4. Interface instability • 5. Short Large Amplitude Magnetic Pulsations

  34. Diffuse upstream ions Paschmann et al. 1981

  35. Free energy due to relative streaming of diffuse upstrem ions and solar wind excites ion - ion beam instabilities in the upstream region

  36. Electromagnetic Ion/Ion Instabilities Gary, 1993 Ion/ion right hand resonant (cold beam) propagates in direction of beam resonance with beam ions right hand polarized fast magnetosonic mode branch Ion/ion nonresonant (large relative velocity, large beam density) Firehose-like instability propagates in direction opposite to beam Ion/ion left hand resonant (hot beam) propagates in direction of beam resonance with hot ions flowing antiparallel to beam left hand polarized on Alfven ion cyclotron branch Ion distribution functions and associated cyclotron resonance speed.

  37. Upstream Waves: Resonant Ion/Ion Beam Instability Backstreaming ions excite upstream propagating waves by a resonant ion/ion beam instability Cyclotron resonance condition for beam ions dispersion relation assume beam ions are specularly reflected ( in units of , in units of ) Wavelength (resonance) increase with increasing Mach number

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