Scales at High Mach Number Quasiperpendicular Shocks and

Problem of Electron Heating

Vladimir

KRASNOSELSKIKH

LPC2E / CNRS-University of Orleans

S.J. Schwartz,

D. Sundqvist, F. Mozer

Electron Heating Scale at High Mach Number Quasiperpendicular Shocks

Plan

Introduction

1. Shock front structure

2. Small scale structure of the electric and magnetic fields

3. Scale of electron heating

4. Conclusions

Collisionless shocks : Critical questions

Quasiperpendicular shock

Thermalisation Variability Particle Acceleration

scales

electrostatic potential

ion reflection

species

partition

fine structure

structure

(ripples ?)

response to upstream conditions

non-stationarity

ion acceleration

electron acceleration

Collisionless shocks : new results from Cluster

Earth’s bow shock

Tsurutani and Rodriguez, 1981

Magnetospheric regions studied by Cluster

Magnetopause

Bow shock

Solar wind

Polar cusp

Auroral zone

Plasmasphere

Initial idea of the shock front structure: dispersion versus nonlinearity in the presence of the weak dissipation

Precursors in sub-critical shocks and early models (Sagdeev, 1961, 1964)

The structure is formed as a result of counter-balance between

nonlinearity and dispersion in the presence of the weak dissipation

Quasiperp Shock profile (heritage of ISEE)

As supposed for subcritical shocks

ISEE and simulations: supercritical quasi-perpendicular shocks: the dissipation is due to reflected ions

How does it change the role of the dispersion and nonlinearity?

Phase velocity dependence of oblique fast magnetosonic (whistler) waves upon the wavenumber

If shock structure is similar to dispersive nonlinear waves then

Gradient catastrophe of nonlinear upstream whistler

Above whistler critical Mach number whistler precursor becomes nonlinear

1/ 2

| cos |

(2 / )Bn

nwe i

Mm m

Galeev et al., 1988 a,b,c; Krasnoselskikh et al. 2002

Above Mnw shock nonlinear steepening of waves can not bestopped anymore by dispersion and/or dissipation and

becomes non-stationary

Nonlinear whistler critical Mach number

Appeal to experimental data of multi-point measurements: Cluster

What are the right questions to answer making use of the data?

• Does the front steepen with the growth of the Mach number till the scales comparable with electron inertial length?

• What are the characteristic scales of fine structure of the shock front?

• What are the sources of waves observed upstream of the ramp?

• Can we observe direct manifestations of the overturning and reformation?

The answer can be found analysing scales and energy fluxes.

What is the scale of the major transition?

Is the region of strongest gradient determined by the dispersion – nonlinearity effects?

Dispersive model:

precursor and ramp transition are determined by dispersion-nonlinearity and scales as several c/ωpe

(electron inertial length)

Magnetic field ramp thickness (Hobara et al, 2010)

Magnetic field ramp grasient (Hobara et al., 2010)

Magnetic ramp thickness statistics (Mazelle et al., 2010)

PRL, 2012

PRL, 20122012

Electron heating (Schwartz et al., 2011)

Electron heating (Schwartz et al., 2011)

Electron heating (Schwartz et al., 2011)

Electric field on the interval 22:15:30-22:15:40

More details 22:15:33-22:15:34

Sundkvist et al., AGU 2012

• The heating can be super-adiabatic as well as sub-adiabatic

• Parallel and perpendicular temperatures grow on the same time scale

• The process is determined by the presence of the small scale electric field bursts

Small scale jumps of the electric field

• Thank you for your attention

• More details on seminar in September