INTERACTION BETWEEN SOLITARY STRUCTURES IN A MAGNETIZED, PLASMA-LOADED WAVEGUIDE

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INTERACTION BETWEEN SOLITARY STRUCTURES IN A MAGNETIZED,

PLASMA-LOADED WAVEGUIDE

J. Lynov, P. Michelsen, H. Pécseli, J. Juul Rasmussen

To cite this version:

J. Lynov, P. Michelsen, H. Pécseli, J. Juul Rasmussen. INTERACTION BETWEEN SOLITARY STRUCTURES IN A MAGNETIZED, PLASMA-LOADED WAVEGUIDE. Journal de Physique Col- loques, 1979, 40 (C7), pp.C7-567-C7-568. �10.1051/jphyscol:19797274�. �jpa-00219261�

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JOURNAL DE PHYSIQUE CoZZoque C?, suppZ&rnent au n07, Tone 40, JuiZZet 1979, page C7- 567

INTERACTION BETWEEN SOLITARY STRUCTURES IN A MAGNETIZED, PLASMA-LOADED WAVEGUIDE

J.P. Lynov, P. Michelsen, H.L. PBcseli and J. Juul Rasmussen.

Association EURATOM

-

Risd National Laboratory, DK-4000 RoskiZde, Denmark.

Introduction: Two different types of non- linear electron pulses have been observed experimentally and in numerical simulations /1-2/, namely, a compressional structure corresponding to a negative potential which was identified as a Korteweg-de Vries soliton, previously observed and described by Ikezi et al. /3/, and a pulse with posi- tive potential indicating a deficit of electrons which we refer to as an electron hole. This electron hole appears as a BGK equilibrium /4/ and our numerical simulations show that it is associated with a vortex-like configuration in phase space, thus resembling the almost stationary structures observed in a number of computer simulations of the electron two-stream in- stability /5/. In this paper we report observations of the mutual interaction between electron holes and their interaction with the M V solitons.

Experiment: The experiment was conducted in the Rise Q-machine operating in the single-ended mode. A caesim plasma was produced by surface ionization on a hot tantalum plate, 3 cm in diam. A homogeneous magnetic field of 0.4 T strength confined the plasma radially. Electron and ion tem- peratures were % 0.2 eV and plasma densi- ties were in the range lo6-107 ~ m - ~ . Col- lisions were entirely unimportant for the pulse propagation. The plasma was sur- rounded by a grounded cylindrical brass tube of 4 cm inner diameter acting as a waveguide. Pulses or waves were excited by means of a terminating brass tube 30 cm in length /6/. We obtained a dispersion re- lation for small amplitude electron oscil- lations /2/ that fitted very well to the Trivelpiece-Gould expression including thermal effects

with w = the electron plasma freq., a = the plgsma radius/2.4

,

^{and ve}⁼

VT/m' _- .

By exciting short negative pulses at x = 0.3 m with amplitudes of the order of 1 V and durations of the order of a plasma period (= 2 ~ / 0 ) we obtained the traces of the spatialpdevelopment of the measursd potential variations shown in Figs. 1 and 2. In Fig. 1 we applied two pulses (a1 )

to the tube creating two solitons ( S

'f

and two holes (Hl12). We see that S2 1 1 2

passes right through Hl causing only a phase jump of H1. In Flg. 2 a short pulse followed by a long tail was applied, creating two holes (H1 2 ) with a small velocity difference. We se8 that the holes attract each other and coalesce, remaining toge- ther for the total length of the tube. If the two holes were created so that they moved against each other in the laboratory

system, they were then observed to pass through each other.

Simulation: In order to make a numerical simulation of our experiment we used the program described in Ref. 7 which employs the particle-in-cell method with a leap- frog scheme for the movement of 50,000 simulation particles. The electric potential was calculated from Poisson's equation

Fig. 1 Fig. 2

in the form

appropriate for a strongly magnetized plasma in a waveguide where only the lowest radial mode is considered. In (2), n and no are the electron and ion densi- ties respectively, where the ions are as- sumed to be immobile. The total energy of the system was calculated at each time step and we found energy conservation to be better than 2%. Figs. 3-4 show the tem- poral development of the potential varia- tion and the phase space. Here

a.

=

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797274

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--

'P 'Po

-

v ^--^'4'

Vth 'PO

Fig. 3

%m(w a) */e, AD = t e electron Debye length, and

'yth

= (ZT/m)'. In Fig. 3 the situa- tion 1s similar to that in Fig. 1. We observe that the soliton S2 passes through the hole H

,

each being virtually unaffect- ed. Some o$ our simulations indicate, how- ever, that the hole can experience a small phase jump and velocity increase when the soliton passes through it. Fig. 4 shows a case similar to that of Fig. 2, and again we observe the attraction and coalescence of the two holes, H and H2. As in the experiment the simulahon shows that two holes pass through each other if their velocities are opposite in the laboratory system.

Conclusion: We have investigated the interaction of two different types of solitary structures, namely a KdV soliton and an electron hole, in an essentially one-dimen- sional system. We observed that the soliton and the hole will pass through each other with very little disturbance, similar to the case of two solitons /3/. On the other hand, two holes will coalesce if their relative velocities are small, and pass through each other for large relative velocities. Finally, we should like to point out that the electron hole may be important for the description of Langmuir

Fig. 4 References:

/1/ K. Saeki et al., Phys. Rev. Lett. (in press).

/2/ J.P. Lynov et al., Physica Scripta (in press).

/3/ H. Ikezi et al., Phys. Fluids

2

(1971) 1997.

/4/ I.B. Bernstein et al., Phys. Rev.

108

(1957) 546.

/5/ H.L. ~ e r k et . al.

,

Phys. Fluids

13

(1970) 980.

/6/ K. ~ a e k i , J. Phys. Soc. Japan

35

⁽¹⁹⁷³⁾

251.

/7/ V. Turikov, Ris@ Rep. No. 380 (1978).

/8/ T.H. Dupree, Bull. &. Phys. Soc.

23

(1978) 869.

turbulence in the case of strong coupling /2 t 8/.