D. Tskhakaya

G. Kawamura

O. Ishihara

Y. Tomita

Tomita,  Y.

Kawamura,  G.

Ishihara,  O.

Tskhakaya,  D.

NIFS-Repository (National Institute for Fusion Science)

 Dynamics of Plasma Particles to Spherical Probe  in Weak Magnetic Field   Tomita, Y., Kawamura, G., Ishihara, O. (Yokohama National Univ.), Tskhakaya, D. (Univ. Innsbruck)   Charged particle orbits of j-th species (j = e, i) in the uniform magnetic field are investigated in the cylindrical coordinates (ρ, θ, z), where the magnetic field B0 is applied to the axial z-direction. The electric probe is located at the origin with the radius Rp and the applied voltage Vp. The charged particle with the charge qj starts to move from the initial position (ρ = bin, θ = 0, z = zin) with the velocity(υρ = υθ = 0, υz = υ j, in ) . The plasma shielding effect due to the plasma sheath is introduced by the Debye-Hückel formula       φ =RpVprexp[−δsc(r − Rp )λD] : r ≥ Rp , (1) where λD and δsc are the plasma Debye length and the shielding factor, respectively. The normalized equations of motion of the j-th charged particle in this system are following: ρ direction:      d2ρdt 2=α j2ρ(1r 3+ ζscr 2)exp(−ζscr ) +μ j241−ρ 4ρ3, (2) and z direction:       d2zdt 2=α j2z (1r 3+ ζscr 2)exp(−ζscr ) . (3) where the distances, velocity and time are normalized by the impact parameter bin, the initial speed υ j, in  and  bin/ υ j, in , respectively. The system in the absence of magnetic field is determined by the parameter αj,      α j ≡q j RpVpbin/ εin, j , εin, j =mj2υ j, in2 , (4) which is the ratio of the electrostatic potential energy at the distance of the impact parameter to the initial kinetic energy εj,in and the parameter ζsc,       ζsc ≡ δsc / λD , (5) which indicates the plasma shielding effect. The parameter μj indicates the effect of the static uniform magnetic field, μ j ≡ bin /mjυ j, inq j B0, (6)which is the ratio of the impact parameter bin to the Larmor radius with respect to the initial speed  υ j, in . Here mj is the mass of the charged particle, r is the radial position of the particle  (r2 = ρ2 + z2 ) .  The parameter μe of the electron is much larger than that of the ion for the case of ions with the sound speed cs and the thermal speed of the electron  υthe :     (μeμi)2 = ( miυi, inZimeυe, in)2  (micsZimeυthe)2 mime1 , (7)where Zi is the charge state of the plasma ion. This relation indicates the effect of the magnetic field on the ions is much smaller than that on the electrons. In this section we investigate the electron orbits and the electron absorption cross-section to the electric probe. The typical orbit of an electron near the probe with negatively applied voltage, which is located at the origin (ρ = z = 0), is shown in Fig. 1, where αe = 1.0, μe = 0.1 and ζsc = 0, which corresponds to dynamics in the Coulomb potential. The electron in the presence of the axial magnetic field (solid line in Fig. 1) approaches closer to the probe than that in the absence of magnetic field. Here the initial position is set far from the probe position, where the radial potential is negligibly small. The electron, which starts motion along the axial direction, gains a radial velocity due to the radial electric field of the probe. The Lorentz force due to the radial velocity pushes an electron to the azimuthal direction. Therefore, the magnitude of the azimuthal velocity is the first order of the strength of the magnetic field. This azimuthal velocity makes the centrifugal force and the radial Lorentz force due to the axial magnetic field. Therefore, these radial forces are the second order of the magnetic field. Thus the magnetic field has the second order effect on the orbit without magnetic field, see Eq. (2). As a result the radial force balance of the particle between a centrifugal force and a Lorentz force determines the radial motion of a charged particle.   Fig.1 Typical orbit of an electron near the negatively applied probe voltage for the case αe = 1.0, μe = 0.1 and ζsc = 0. The solid and dashed lines are the orbits with and without magnetic field, respectively. : with B0 : without B0 400§16. ynamics of Plasma Particles to Spherical Probe in Weak Magnetic FieldTomita, Y., Kawamura, G.,  Ishihara, O. (Yokohama National Univ.),  Tskhakaya, D. (Univ. Innsbruck)

Dynamics of Plasma Particles to Spherical Probe in Weak Magnetic Field

Dynamics of Plasma Particles to Spherical Probe in Weak Magnetic Field

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