To Kinetic Modeling of Solar Wind over Magnetoactive Regions and Beyond

1. To Kinetic Modeling of Solar Wind over Magnetoactive Regions and Beyond V.Gubchenko (1), V. Zaitsev(1), H.Biernat (2), M. Khodachenko (2), and H. Rucker(2) 1) Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod, Russia, (2) Space Research Institute, Austrian Academy of Sciences, Graz, Austria E-mail: ua3thw@appl.sci-nnov.ru vladimir.gubchenko@assoc.oeaw.ac.at ABSTRACT This work concerns with modelling of 3D structures of corona and its dynamics in terms of the plasma kinetic theory (Vlasov equation ) of a hot current carrying collisionless plasma with double flows . Our models of hot collisionless stellar (solar) corona and wind are based on Vlasov equation. We have polar magnetic regions with a “parallel” expansion: non current-carrying (CC) plasma and high speed wind as well as equatorial regions with a “perpendicular” expansion: a CC plasma and a low speed wind. The polar regions are under electrostatic and prescribed magnetic fields action (ambipolar expansion). Globally the system is described by resistive Volt-Ampere and capacity Volt-Coulomb characteristics. The equatorial region with unprescribed magnetic field is under electromagnetic action; we have formation of a CC plasma with a fine structure of magnetic field. The CC region is described by the diamagnetic and resistive current parts and it is treated by inductive Weber-Ampere characteristics. The CC plasma has a diamagnetic scaling parameter - magnetic Debye scale. We have three regimes for eddy currents dynamics in the equatorial region: resistive, diamagnetic, and quasi-current-free (QCF). The diamagnetic regime is a quasistationary state and we model a stellar current disk by a diamagnetic Harris sheet submerged in a flow of a high speed plasma. The 3D resistive structures: streamers and CME are results of the tearing and stratification electromagnetic instabilities in the sheet. Nonstationary nonlinear flare type events with particle acceleration are treated in the QCF regime. 2. DIAMAGNETIC STATIONARY STATE OF SOLAR CORONA Above is a double humped additive type VDF for the plasma in the heliospheric sheet when CCP is in a stationary diamagnetic state. It is a Harris type current sheet with the plasma flows inside. The sheet thickness is expressed via the anisotropy parameter kax of the CCP. Fig. 5. 2D approximation of the solar corona by a diamagnetic neutral current sheet which is submerged into a high speed Solar wind flow. On the left-hand side of the figure a velocity profile u(x) is shown. The regions 1 and 2 correspond to the low speed flow and to the high speed flow respectively. On the right-hand side is the plasma density profile n(x) with a maximum at the neutral sheet where Br(x)=B th(x/L) changes its direction and where the current disk is located. Quantity L is the neutral current sheet thickness. Fig.6. Two-dimensional fda(vx,vz,x) = fca+ fwa and one-dimensional f(vz,x) cross-sectional view of the resulting VDF for the diamagnetic stationary state. We see VDF for the regions with the low, intermediate, and high speed. Direction z is defined by the magnetic field vector B0 and bulk flows uc and uw. Direction y is defined by the direction of the current j0. These pictures we associate with the Helios mission data on VDFs in the Solar Wind plasma. Additional details on the VDFs will appear in dynamical state. 1. COLLISIONLES HOT CURRENT CARRYING PLASMA WITH FLOWS There are two ways to treat Solar corona and Solar Wind (SW): MHD and Kinetics. We develop here Vlasov kinetic ap-proach paying attention to the physics of heliospheric current sheet plasma. Fig. 1. A 3D view of solar corona with fine structure elements out of ecliptic plane during the minimum of the solar cycle. Here {x,y,z} is the local Cartesian coordinate system located in the ecliptic plane, r, q, f are the heliocentric spherical coordinates. 1 is a circular region of closed magnetic structures with a set of magnetic islands- transients; 2 is a circular region of open magnetic field lines with rays, magnetic ropes elements, streamers; 3 is a circle of the solar radius r0 on the ecliptic plane where active regions are located; 4 is a circle with radius rn > r0 in the ecliptic plane where transition from the magnetic islands to the magnetic rope structures takes place. 3. DIAMAGNETIC AND RESISTIVE STATE OF DYNAMICAL SOLAR CORONA Stationary diamagnetic configuration with the current sheet and a double humped plasma VDF has an internal anisotropy ka . This dimensionless anisotropy parameter ka depends on the value and orientation of the wave vector k and parameters of the diamagnetic VDF: the current associated drift velocity ua along y, difference of velocities in plasma flows Du =uw – uc and the ratio bw=nw /nc . The anisotropy is the source for the Weibel type instability of the transverse electromagnetic (TEM) plasma mode. The TEM mode produces perturbations of initial diamagnetic configuration by the diamagnetic current jd1 and by the resistive current jr . In the Harris sheet plasma this mode has different topology depending on the direction of wave vector k. Dispersion equation for TEM mode in plasma with the anisotropy ka has the following form Fig.2. (to the left and above) the Solar Corona / Solar Wind electric circuit with current I and charge separation Q. Polar regions of the SW expansion form capacitor C of the circuit. The ecliptic plane with the heliospheric current sheet disk containing a spiralling current I, forms inductance L of the circuit. The electromotive force excites current in the load R, produces magnetic flux F,and charges capacitor. In the top is the electro technical scheme of the heliosphere. Further we study the physics of L and R elements. The scale rDM is the Magnetic Debay scale in plasma with anisotropy ka (k/|k|). It describes a scale for the screening of an external current by the diamagnetic plasma currents. When ka>0 basic scale of structures is rDM. When ka<0 plasma is stable.We calculate anisotropy via calculation of the diagonal component et1(w,k) of the dielectric tensor eof the plasma with the VDF fda. The scale rDM(k/|k|) strongly depends on orientation of the wave vector k of perturbations. When k =kzz0 then ka=kay and rDM =rDMy, if k =kyy0, then ka=kaz and rDM =rDMz . When k =kxx0 , then ka=kax and rDM =rDMx=L. When ka<0 plasma is stable to perturbations. The ratio nc kay +nw kaz = 0, reflecting the symmetry in action of the currents and flows takes place. Fig.7. The decay rate wi(k) of the TEM mode in the anisotropic plasma in the quasi-stationary limit |wi(k) /kVa |<< 1. The quasi-current-free approximation (dotted line) is valid on the interval k rDM <<1 where in the dynamical regime the diamagnetic current jd1 is compensated by a current jr of accelerated particles. The inequality jd1 >> jr holds true in the region of stability D where krDM =1 , while the ratio jr >> jd1 takes place in the region R with k rDM >>1 where the diamagnetic effects are damped. The dispersion curve of a current-free isotropic plasma is shown by the dotted line in the lower part. Fig.8. Topology of the magnetic field in the heliospheric current sheet system with two types of excited the TEM modes: tearing and stratification (kink sausage) mode. Tearing mode is characterized by A=Ayy0 and k =kzz0(characteristic scale of structures rDM =rDMy). Stratification mode is characterized by A=Azz0and k =kyy0 (characteristic scale of structures rDM =rDMz). Fig.4. (the low left corner) Typical 2D electromagnetic structure of fields inside the heliospheric current sheet during “perpendicular” expansion of plasma relative the magnetic field lines and the eddy electric field. Charged particles have a component of velocity V|| along, and a component VT perpendi-cular to the magnetic field lines. Velocity Distribution Function (VDF) is shown in the cross-section to magnetic field where Va is a thermal velocity. There are “slow” particles with velocity |VT|<V´ which are responsible for theresistivity in plasma. This particles are mainly under action of the electric field E=-(1/c)dA/dt. They produce the current jr. There are “fast” diamagnetic or nonresonace particles with ve-locity |VT|>V´. These particles are under action of the magnetic field B=rotA. They produce the current jd. Characteristic velo-city V´ = r´/t´<<Va is defined via characteristic scale r´=k-1 and time t´=|w|-1 of the process in the CC plasma. This process we treated in Vlasov kinetic approach as it cannot be treated by the MHD methods.| Fig.3. (above) A volume of the current carrying plasma (CCP) and the SW plasma flow in two cases. 1) The polar magnetic region with “parallel” expansion of non-CCP along the magnetic field lines, where the process is under action of the electrostatic field j. 2) The equatorial heliospheric current sheet region with “perpendicular” to magnetic field expansion of a CCP, where particles are weakly magnetized and move perpendicular to the equatorial magnetic field. The particles are mainly under action of electromagnetic field describe by the vector potential A. In this region fine structure elements of the solar corona are produced. We get stabilisation effect on current instability from flows in the sheet. Scale of fields increased by flows. 4. CONCLUSION We associate tearing mode with magnetic islands and CME formations. Stratification mode is formed by magnetic ropes and we associated it with a streamer belt around the Sun. According to the ratio nc kay +nw kaz = 0 we get tearing mode unstable (kay>0) when the stratification mode is stable (kaz<0). In the case of the tearing mode stability (kay< 0) we have unstable stratification mode (kaz>0). It is natural to propose that heliospheric plasma is at a stable state kay =kaz = 0 when double humped plasma flows in CCP are balanced by electric currents. We get stabilisation effect on flow instability from currents in plasma. Scale of fields increased by current. REFERENCES • Gubchenko, V.M., Fizika Plasmy, 1982, 8(5), 1040 • Gubchenko, V.M., H.K. Biernat, M, M. Goossens, Adv. Space Res., 2003, 31, No. 5, 1277. • Gubchenko, V.M. Fizika Plasmy, 1985, 11(4), 467. • Gubchenko, V.M., M.L. Khodachenko, H.K. Biernat,V.V. Zaitsev, H.O. Rucker, Hvar Obs. Bull, 2004, 23.