J. Plasma Fusion Res. SERIES, Vol.2 (1999) 157-160

Formation of dc Potential Structure Due to Current-Driven
Electrostatic lon-Gyclotron Instability
ISHIGURO Seiji and SATO Tetsuya
Theory and Computer Simulation Center, National Institute for Fusion Science

Toki-shi 509-5292, Japan(Received: 22 February 1999 / Accepted: 15 April 1999)

Abstract
Formation of dc potential structure due to current-driven electrostatic ion-cyclotron instabilities has
been investigated by means of an open boundary two-and-a-half dimensional electrostatic particle in cell(PIC) simulation model. A dc potential difference is built up as a fluctuation associated with an ioncyclotron wave induced by streaming electrons grows. A V-shaped dc potential structure is created for abell-shaped electron stream, while the dc potential does not have a structure across the magnetic field fora uniform electron stream.

Keywords:
particle simulation, electrostatic ion-cyclotron instability, potential formation, aurora, kinetic-selforganization.

1. Introdustion
Formation of electrostatic potential structures indc potential difference along the magnetic field due tothe current-driven instability in an open boundary

magnetized plasmas is as yet a challenging problem forsimulation model. Furthermore, we have succeeded indemonstrating that a V-shaped dc potential structure iscreated by a current-driven electrostatic ion-cyclotron
instability in the case of bell-shaped electron stream

generating accelerated charged particles in a spaceplasma and controlling particle confinement in a fusionoriented plasma device []. In particular, many spaceobservations support the theory that auroral electrons are[l]. It is also interesting that the formation of dc

accelerated by an electric field above the ionosphere [2-potential structure due to a kinetic instability from theview point of the kinetic self-organization [2]. In thispaper, we present the time evolutions of dc potential
structure accompanied by current-driven electrostatic
ion-cyclotron instability for the cases with a spatially
uniform electron stream and a bell-shaped electron

4]. A current-driven electrostatic ion-cyclotron

instability has been paid much attention as a candidate
for formation mechanism [5,6]. In fact, it is reported thata V-shaped potential structure and an electrostatic ioncyclotron wave are simultaneously present above theauroral ionosphere [7]. Although many computer
simulations concerned with an ion-cyclotron instability
have been performed [8,9], they did not succeed indemonstrating the creation of a dc potential differencealong the magnetic filed by the instability.
In our previous papers tl0,l ll we have shown thatthe growth of an ion-cyclotron wave and creation of astream.

2. Simulation Model
We have employed a two-and-a-half dimensional

particle in cell (PIC) simulation model with a selfconsistent open boundaries [1,13]. A self-consistent@1999 by The Japan Society of Plasma
Science and Nuclear Fusion Researchr57

Ishiguro S. et al., Formation of dc Potencial Structure Due to Current-Driven Electrostatic Ion-Cyclotron Instability

In order to see the relation between the growth of
the ion-cyclotron wave and the increase of the dc

open boundary condition is applied to the x direction,
while a periodic boundary condition is applied to the ydirection. An extemal uniform magnetic field is pointing

potential difference, we show the time evolutions of theion density fluctuation of the mode with ftxpi = 0.086
and k 1pi = 0.55 (a) , which is a typical unstable mode to

into the x direction. The system is assumed to be divided
in segments in the y direction where each segment is

the ion-cyclotron instability in our simulation

assumed to be connected to an external constantgenerator, and thus the particle influx at the x = 0 and "rparameters, and the potential difference along themagnetic field which is averaged over the y direction
and four times of the plasma period (b) in Fig. 2. The
ion density fluctuation rapidly grows in the initial stage.
The potential difference goes up with an increase in the= L, boundaries is controlled in such a way that the net

flux is kept constant in each time step in each segment.
This procedure is applied for electrons, while thereflection boundary condition is applied for ions.
The ion motion is followed in the two dimensional
real space and the three dimensional velocity space,
whereas we adopt the drift kinetic approximation for-0.04electrons.

Simulation parameters are as follows: The systemsizes are L , = 512 i,p" and L, = 128 lp" and 512 x 128
spatial cells are used, where i.p" is the Debye length.
The system is divided in l6 segments in the y direction.

0"00

0"04

€0IT*
128

{64The ion to electron mass ratio is 400 and thetemperature ratio is ll2. The electron cyclotron

512

frequency @""= 5 too" and the ion cyclotron frequency is@.i = 0.0125 o)*, where alo" is the plasma frequency. At0.04

r = 0, 67108864 ions and electrons are uniformlyv/lr**64

b 0.00

distributed in the system. The ion velocity distribution isa Maxwellian, while the electron velocity distribution isa shifted Maxwellian with drifting into the x direction.
In this paper we present the results of the cases with a-0.oo6

258512128

uniform electron stream and a bell-shaped electronfMstream. For the uniform electron stream case, we have
performed with the electron drift velocity v6"/v1" = 0.8,
where v," is the electron thermal velocity. For the bellshaped electron stream case, electron drift velocity isgiven by v6(y)/vr" = 0.6 - 0.2 cos (2ny/L,).

512
0.04

It is to be noted that ion acoustic wave is not

vfls*=64

b 0.00

unstable and electrostatic ion-cyclotron wave is unstablein these plasma parameters.

-0 0o6

3. Simulation Results

256

512

128

a

First of all, we present the results for the case of thespatially uniform electron stream with v6./v," = 0.8.
Figure I shows the time evolution of the dc potential
profile which is averaged over the period of the ioncyclotron oscillation. We can see that the potential
gradually goes up to the downstream region along themagnetic field. This potential difference along thed64od{

L512,0.04ffi* 0"0omagnetic field grows with time and the potential
difference becomes eAQl7":0.05 at ar*r = 2000. It is to-0"04$

be noted that there is no significant potential structure
across the magnetic field.

256

512

Fig. 1 Time evolution of dc potential profile for the casewith a uniform electron stream.
r58

Ishiguro S. et al., Formation of dc Potencial Structure Due to Current-Driven Electrostatic Ion-Cyclotron InstabilityeAQlT" = 0.02 at;r = 100 ,tr.p". In this case, the wave
amplitude is larger in the fast electron stream region (y= Lyl2) than in the slow electron stream region (y = 0,fluctuation accompanied by the instability in the initialstage. At ap.t =2000 the growth of the potential
difference saturated, although the growth of thefluctuation level continues. The potential differencelr), and thus the potential difference along the magnetic

along the magnetic field lines across the system is abouteAQlT":0.05. Potential difference along the magnetic
field lines may be created by the anomalous resistivity.
The anomalous resistivity can be calculated from therelation 4 = eE lnoe2 v* = e (AQl L,)l nse2 v*r. Using theabove results with eAQlT" - 0.05, L"= 512 hD", vd"=
0.8 v,", one can get rlleo= I x l0-4, where 4e - 4n/04..
Next, we show the time evolution of the dc

field is larger in the fast electron stream region than in
the slow electron stream region. The ion-cyclotron

potential profile for the case with the bell-shaped

be created.

electron stream. Figure 3 shows the time evolution of
the dc potential profile which is averaged over the

The potential difference obtained in this simulationis quite small. However, the potential jump increases as
propagating in the downstream region. Thus it is likely

instability causes the ion perpendicular heating as wellas the ion transport across the magnetic field. Since theinstability is stronger in the fast electron stream region
than in the slower electron stream region, the fastelectron stream region becomes electron rich. As aresult, the potential well across the magnetic field may

period of the ion-cyclotron oscillation. A V-shapedthat a larger potential difference may be created for apotential structure which is vaguely seen in the upstream
region at o)o.f = 500 grows with time, and then clearlylarger and longer system. If we assume that the potential
difference is proportional to the system length, one canget kV potential difference for T" = | eY, n" = 102 cm-3,formed at o)pet = 2000. The potential difference along
the magnetic field is eAQlT" - 0.04. Potential well isalso observed across the masnetic field. Its deoth isand several thousand kilometers anomalous resistivitva)
1o-5c.l10-6
J

tr10-7
1o-8Op"tb)'0.06

Potential Differencec)

Fe 0.03()

0.00%.tFig. 2 Time history of ion density fluctuation (a) and potential difference along the magnetic field (b) for the case with auniform electron stream.
159

Ishiguro S. et al., Formation of dc Potencial Structure Due to Current-Driven Electrostatic Ion-Cyclotron Instabilityregion [4], which is consistent with the auroral electron

4. Summary

acceleration.

We have investigated that the time evolutions of dc
potential structure created by current-driven electrostatic

ion-cyclotron instabilities by means of an open

0.00

boundary two-and-a-half dimensional electrostatic
particle in cell (PIC) simulation where the simulation

0.04

s$trfesystem is connected to constant current generators. It isshown that the dc potential difference along themagnetic field gradually increases with an increase in128
E

the fluctuation accompanied by electrostatic ion-*64

cyclotron waves due to the instability. The electrostatic
potential increases from the upstream boundary to thedownstream boundary. While there is no significant
potential structure across the magnetic field for the casewith the uniform electron stream, a V shaped potential
structure is observed to srow with time for the bell-0d0.of

vfl"--G4

b 0.00{.0uf256

shaped electron stream.

512

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128

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Fig. 3 Time evolution of dc potential profile for the casewith a bell-shaped electron stream.

(l978).

r60