J. Plasma Fusion Res. SERIES, Vol.2 (1999) 389-392

On the Microscopic Basis of the Negative Differential
Resistance
LOZNEANU Erzilia, POPESCU Sebastian and SANDULOVICIU Mircea
Department of Plasma Physics, "Al. I. Cuza" University,
Blvd. Copou, No.II, 6600 lasi, Romania(Received: 7 December 1998 / Accepted: 6 May 1999)

Abstract
Abrupt transitions and multiple states evidenced in the I(V) characteristic of a Q-machine are
analyzed in the frame ofan intermittent self-organization scenario able to reveal new aspects concerning
the negative differential resistance behavior of a non-linear conductor.

Keywords:
non-linearity, instability, self-organization, negative differential resistance, oscillations

radical changes in science concerning systems

1. Introduction
The aim of this paper is to emphasize that the"vital" part of an oscillator working with a gaseous

exhibiting abrupt transitions and a multiplicity of states[8], we explain the non-linear behavior of the Qmachine plasma considering an intermittent scenario ofself-organization in the frame of which the creation ofconductor showing negative differential resistance(NDR) is located in the unstable space charge

double layers (DL) has its origin in the symmetry
breaking and spatial separation of the excitation andionization cross section functions [2-5]. Because theconfiguration formed by self-organization in front of theanode. Based on these results and also on many strong
similarities between a plasma oscillator and a Gunn
oscillator [], we propose a mechanism that explains theassemblage of a DL by the above mentioned phenomena
is a cumulative process, its presence is not excluded in aoccurrence of the NDR in the frame of a new selforganization physical scenario [2-5] potentially possible
in all non-linear conductors.

Q-machine. Evidently in such conditions the time span

2. Experimental Devace and Results
The experiment was performed on a Q-machine
schematically presented in Fig. l. The low-density
plasma of a Q-machine is traditionally consideredcollisionless. Nevertheless, as it was recently emphasized [6,7], the inelastic collisions are not only
possible but also obviously necessary for explaining theastonishing similarities between the strong non-linear
behavior of the plasma created in a Q-machine and thatof a plasma in which inelastic collisions are present.
Takine into account the above said and also theFig. 1 The O-machine working as a plasma oscillator.

@1999 by The Japan Society of Plasma
Science and Nuclear Fusion Research

C o rr e s pondin g autho r' s e - mai I : e rlo z@ uaic. ro389

Lozneanu E. et al., On the Microscopic Basis of the Negative Differential Resistancenecessary to produce the space charge separation
depends, for a fixed current intensity, on theconcentration of neutrals. This is the reason why theI(V) characteristic of a Q-machine very clearly reveals
strong non-linearity only for low currents and plasma

increases so that 1 remains nearly constant although V

gradually increases (a stationary DL is that whose
location with respect to CP depends on V when the otherparameters are maintained constant). Another very
important state, directly related to the mechanism of theNDR, appears when V = V3. During this state l becomes
periodically limited (Fig. 3). This characteristic wasobtained by linear increasing of the voltage of theexternal dc power supply with a slope sufficiently highto reveal the temporal variations of 1.

densities (Fig. 2).
For elucidating the physical processes related to thenon-linearity emphasized in this (V) characteristic we
put forward the assertion that the experimental results
obtained from a collisional plasma are a guide tounderstand also the phenomena taking place in a Q-

In order to explain the weak modulation of 1
appearing when V = V, we remind that in a collisional
plasma such phenomena are related to the successive
generation and disruption of DLs in front of the anode[2-5]. These phenomena appear after the transition of
the stationary DL, located at a certain distance from CP,
into a self-consistent state. During that state it departs
from the CP although V remains constant. Its "motion"away from CP is governed only by internal processes

machine. Consequently we explain the multiplicity ofstates of the plasma created in a Q-machine (revealed inthe I(V) characteristic by the presence of critical points
marked by V with subscript numbers) by considering a"scenario" including a succession of states. The first is
one in which plasma is in thermodynamic equilibrium
and is asymptotically stable. A second state appears
when on the plasma acts an external constraint, in theform of a positive voltage V < V1 applied on the coldplate (CP). In this state the plasma behaves as a normal
conductor, i.e. .l proportionally increases with V. The
following state, that is an "anomalous" one, appears
when y = Vr. In that state 1 decreases in spit of theincreasing V from V1 to V2. This anomalous behavior iscaused by the accumulation of those electrons that havelost their momentum by neutrals' excitation 12-71. The
negative space charge formed in this way in front of theCP acts as a barrier for 1 determining its decrease. The
appearance of the following new state is marked by theabrupt increase of 1 when V = Vz.It appears when a DL,
able to accelerate electrons at energies for which theionization cross section function suddenly increases, isspontaneously created. In the voltage range lV2- V3l theDL is stationary but it departs from the CP when V
increases. During this departure the net negative spacepossible when the electron flux across the DL issufficiently high. The dynamics of the self-consistent
DL produces weak modulations of 1, evidenced in Fig.
3, for every value of V in the voltage range [V3- Va].
During this self-consistent state, the conditions for theformation of a new DL in front of the CP re-appear. The
negative space charge accumulated during the formationof a new DL and that one present in front of the selfconsistent (moving) DL act as barriers for l determining
its decrease (branch a-b in Fig. 3). Simultaneously withthe development of this new DL, the existence
conditions for the formerly self-consistent one cancel sothat it disrupts releasing the opposite space charges fromits two sides. As a consequence, the conductivity of theplasma column suddenly increases determining acorrespondihg increase of 1 and also a diminishing of
the potential difference supported by the plasma column

charge accumulated at the negative side of the DL(branch b-c in Fig. 3). The electrons released during theFig.3Dynamic //V)-characteristic proving theFig. 2 Static l(V)-characteristic of a O-machine. The
plasma density is n = 6.8 1014 m 3.

appearance of weak current modulation under theconditions that the PRI does not appear.

390

LozneanuE.etal., OntheMicroscopicBasisoftheNegativeDifferentialResistanceis the consequence of the disruption of a DL generated
after self-organization in front of the CP. This disruptionis accompanied by a sudden gathering of electrons by
the positive CP and a jump of the potential of theplasma column (except a small region in front of theHP) to a potential value close to that of the CP. In thisway the region where the electrons are accelerated isshifted in front of the HP. Obtaining here the kinetic
energy for which the excitation cross section function
increases suddenly, a new barrier for 1 forms in front of
the HP. This negative barrier departs from HP and, after
running a certain distance, nreets the negative side of thestationary DL localized at a certain distance from CP.
The addition of the net negative space charge carried by
the barrier to that existing at the negative side of thestationary DL transforms this in a self-consistent state
whose dynamics, sustained only by intemal processes, isfinished by its disruption [2-4]. After that the plasma
potential suddenly jumps again to a value closed to thatof the CP. So, the phenomenon cyclically repeats. We
point out that the above described mechanism does notdisruption ofthe self-consistent DL are collected by CP
contributing to the formation of a new DL that repeats
the above described dynamics. In this way thephenomenon becomes a periodical one.

The transition towards the strong /-oscillations,
usually referred as potential relaxation instability (PRI)[8], emphasized in the in the voltage range [Va- V5] ofthe I(V) characteristics shown in Fig. 2 and Fig. 4, is not

related to the presence of a NDR as generally
considered [9], but rather to the appearance of a positive

differential resistance. This is a very important
experimental result because, to the best of ourknowledge, that has not been previously reported. The
amplitude growing process shown in Fig. 4 proves thepresence of a resonance phenomenon. It appears in a Q-machine when the plasma column is able to support a
half-wavelength ion-acoustic standing wave excited byperiodical injection of bunches of positive ions producedin the moment when the DLs, successively generated in
front of the CP, disrupt.
We remind that the similarities between thephenomena observed in a Q-machine and those

involve the suppression of the weak 1 modulations

observed in a Gunn diode are referring to the generation

whose presence is obviously necessary to stimulate theof barriers for 1 at the HP and to their propagationstrong 1 modulations. On the other hand during thestrong 1 modulation the current barriers formed at theHP triggers the injection of a bunch of positive ions in
the disruption phase of the self-consistent DL andconsequently the stimulation of PRI. For higher plasma
density, the weak modulation regime of 1 is compressed(Fig. 5) and the dynamical I(V) characteristic becomessimilar to those of a Gunn diode [].
The last described phenomenology, taking place intowards the CP [8]. The appearance of such barriers for/ was observed in a Q-machine only during the presenceof the strong l oscillations shown in Fig. 4 when V > Vs.
Similar phenomena, but experimentally difficult toreveal, are very probably present also during the weak 1modulations.
In agreement with the above-described phenomenology, the generation of barriers for 1 in front of the HP%v,v(r)Fig. 4 Dynamic l(V)-characteristic proving the transition

Fig.5 Dynamic l(V) characteristic obtained when theplasma density is so high that the transition

from weak to strong oscillations observed underthe conditions that the plasma column length andconcentration are appropriate to support a ion-through the weak / modulation is compressed andthe PRI seems to appear directly.

acoustic standing half wave,391

Lozneanu E. et al., On the Microscopic Basis of the Negative Differential Resistancefront of the CP, clearly proved in a nonlinear plasma

to sustain and control, like a cell membrane, a rhythmicexchange of matter and energy between two regions ofthe plasma column. The rhythmic matter and energy
exchange triggers also the formation of moving current
barriers at the HP and the stimulation of an ion acoustic
half-wavelength standing wave in the plasma column.
We presume that a similar self-organization phenomenon, taking place at the anode of a Gunn diode, triggers

conductor, was not investigated up to now at the anodeof a Gunn diode.
When the voltage applied between HP and CP is
gradually decreased, the I(V)-characteristic shows
hysteresis. That reveals a sort of memory by which thestate of the system depends on its past history. As
generally accepted, such phenomena are characteristic
for complex structures formed after self-organization

the generation of space charge domains at the cathodeand implicitly stimulates oscillations in the resonantcavity suitably connected to it.

tl0l.

3. Conclusions
The similarity between the phenomena observed in

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