On Kinetic Approach to Modeling of 3D Solar Corona and Slow Solar Wind at Heliospheric Current Sheet Plasma

V.Gubchenko (1), V. Zaitsev(1), H.Biernat (2), M. Khodachenko (2), and H. O. 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

ABSTRACTThis work concerns with modelling of 3D structures of corona and its dynamics in terms of plasma kinetic theory (Vlasov equation ) of a hot current carrying collisionless plasma with double flows .

Basic large scale 3D magnetic elements of solar corona are located in a slow solar wind and in a heliospheric current sheet. They are magnetic islands associated with CMEs, and magnetic flux ropes are associated with streamers. Dynamics of these structures is accompanied by acceleration of particles, which can result in type I and type III radio bursts. We study the 3D solar corona in kinetic approach in terms of current carrying collisionless hot plasma with double humped velocity distribution functions. The system under investigation has a certain parameter of anisotropy, and its dynamics is considered for three specific cases: resistive, diamagnetic or quasi-stationary, and quasi-current free. We suppose that the current sheet corresponds to the diamagnetic case, when diamagnetic currents are stronger than resistive currents associated with particle acceleration process. A 3D dynamical structure of the corona is formed as a result of relaxation or instability of the initial 2D diamagnetic state; it is a neutral current sheet submerged into diverging plasma flow. The appeared 3D structure elements are result of an e.m. plasma anisotropy instability. They have two orthogonal polarizations: tearing mode, which forms CMEs, or stratification mode forming streamers belt.

1. INTRODUCTION (COLLISIONLES HOT CURRENT CARRYING PLASMA WITH FLOWS)

Fig. 1. A 3D view of solar corona with fine structure elements out of ecliptic plane during its minimum. Here x,y,z are Cartesian coordinate system located on ecliptic plane, r, , are spherical coordinates, and r0 is the Sun exospheric radius. 1: It is a circular region of closed magnetic structures with a set of magnetic islands - transients excitation, 2: It is a circular region of open magnetic field lines with rays, magnetic ropes elements, streamers, 3: A circle with Sun radius r0 on ecliptic plane where active regions are located. 4: A circle order with radius rn on ecliptic plane where transition from magnetic islands to magnetic rope structures takes place.

Fig.2. 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. Ecliptic plane with heliospheric current sheet disk with spiralling current I forms inductance L of the circuit. Electromotive force excites current in the load R makes magnetic flux and charges capacitor. On the right side is electro technical scheme of the heliosphere. We study further in kinetics physics of the LR elements.

Fig.3. Volume of the CCP current carrying plasma (CCP) SW plasma flow in two cases. The polar magnetic region with “parallel” expansion of non CCP along magnetic field lines where process is under action of electrostatic field . The equatorial heliospheric current sheet region with “perpendicular” to magnetic field expansion of a CCP where particles are weakly magnetized and move perpendicular to equatorial magnetic field and are mainly under action of electromagnetic field A. This region produce fine structure elements in solar corona.

Fig. 4.Typical 2D electromagnetic structure of fields inside heliospheric sheet during “perpendicular” plasma expansion with magnetic field lines and eddy electric field . Charged particles have components of velocity along V|| and perpendicular component to magnetic field lines VT. It is shown VDF in the crossection to magnetic field where Vis thermal velocity. There are accelerated particles with small velocity |VT|<V´ forming resistivity in plasma. This particles are mainly under action of electric field E=-(1/c)dA/dt and produce current jr. There are diamagnetic particles or nonresonace particles with large velocity |VT|>V´. This particles are under action of magnetic field B= rotA. and produce current jd. Characteristic velocity V´ = r´/t´<<V is defined via characteristic scale r´=k-1 and time t of the dynamical process in CC plasma. This process we treated in Vlasov kinetic approach

and it cannot be treated in MHD terms.|

2. DIAMAGNETIC STATIONARY STATE OF SOLAR CORONA

Fig. 5. A Solar corona in rough 2D approximation by a diamagnetic neutral current sheet which is submerged into a high speed Solar wind flow. On the left side of the figure a velocity profile u(x), region 1 is a low speed flow and region 2 is a high speed flow. On the right side profile n(x) of plasma density with maximum at the neutral sheet where radial magnetic field B(x) =B th(x/L) changes its direction and where current disk is located. Quantity L is the neutral current sheet thickness.

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Fig.6. Two dimensional velocity distri-bution function (VDF) fd(vx,vz,x) = fca+ fwa and one dimensional f(vz,x) cross sctional view of the resulting velocity distribution function (VDF) for diamagnetic stationary state. We see VDF for points in low speed, intermediate region and high speed region. Direction z is defined by vector B0 and bulk flows uc and uw. Direction y is defined by direction of current j0. This pictures we associated with “Helios” data on VDFs in the Solar Wind plasma. Additional details on the VDFs will appear in dynamical state.

3. DIAMAGNETIC AND RESISTIVE STATE OF DYNAMICAL SOLAR CORONA

Fig.7. The decay rate (k) of the TEM mode in an anisotropic plasma in quasi-stationary limit |(k) /kV |<< 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 in the region of stability D where krDM =1 , while jr >> jd1 in 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

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4. CONCLUSION

Fig.8. Topology of magnetic field in the heliospheric current sheet system with two types of excited TEM modes: tearing and stratification (kink sausage) mode in heliospheric sheet. Tearing mode A=Ayy0 and k =kzz0 (characteristic scale of structures rDM = rDMy) . Stratification mode A=Azz0 and k =kyy0 (characteristic scale of structures rDM = rDMz) .

)//(1 222 cr pDM

wcd fff

Above is additive type distribition function for heliospheric sheet plasma particles when CCP is in stationary diamagnetic state. It is a Harris type current sheet with double humped plasma flows inside. The sheet thickness expressed via anisotropy parameter of the CCP.

Stationary diamagnetic configuration with current sheet and with double humped plasma flows has internal anisotropy . This dimensionless anisotropy parameter depends on wave number orientation k and parameters of the diamagnetic VDF: current drift velocities u along y, difference of velocities in plasma flows u =uw – uc and ratio wnw /nc . Anisotropy is the source of the Weibel type instability of the electromagnetic (TEM) plasma mode. The TEM mode produce perturbations of initial diamagnetic configuration by diamagnetic current jd1 and by resistive currents jr . In the Harris sheet plasma this mode has different topology depending on direction of wave number k.

Dispersion equation for TEM mode in plasma with anisotropy . The scale rDM is Magnetic Debay scale in plasma with anisotropy k/|k| and it describes scale for screening of a sample external wire with current by diamagnetic plasma currents. When basic scale of structures is rDM. When plasma is stable.We calculate anisotropy via calculation of the diagonal component t1,k) of the dielectric tensor formed by plasma with the VDF fd.

The scale rDM(k/|k|) strongly depends on orientation of wave number k of perturbations. When k =kzz0 we get y and rDM = rDMy, when k =kyy0 we get z and rDM

= rDMz . When k =kxx0 we get x and rDM =rDMx=L. When plasma is stable to perturbations. We can get ratio nc y +nw z = 0 reflecting symmetry in action of currents and flows.

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)//(1 222 cr ypcDMy

)//(1 222 cr zpwDMz

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 ratio nc y +nw z = 0 we get tearing mode unstable y>0 when we have stable stratification mode z<0, in the case of tearing mode stability y< 0 we have unstable stratification mode z>0. It is natural to propose that heliospheric plasma is at a stable state y = z = 0 when double humped plasma flows in CCP are balanced by electric currents.

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REFERENCES

1. Gubchenko, V.M., Fizika Plasmy, 1982, 8(5), 10402. Gubchenko, V.M. Fizika Plasmy, 1985, 11(4), 467.3. Gubchenko, V.M., H.K. Biernat, M, M. Goossens, Adv.

Space Res., 2003, 31, No. 5, 1277.4. Gubchenko, V.M., M.L. Khodachenko, H.K. Biernat,V.V.

Zaitsev, H.O. Rucker, Hvar Obs. Bull, 2004, 23.

We get stabilisation effect on current insta-bility from flows in the sheet. Scale of fields increased by flows.

We get stabilisation effect on flow insta-bility from currents in plasma. Scale of fields increased by current.

There are two „opposite“ ways to treat Solar corona and Solar Wind: MHD and Kinetics. We develop here Vlasov kinetic approach with attention to physics of heliospheric current sheet plasma at solar corona.