J. Plasma Fusion Res. SERIES, Vol 4 (2001) 532-535

A New InsigGomplex
Department

into the Self-Assemblage Mechanism ofGharge Configurations in Plasmas
LOZNEANU Erzilia* and SANDULOVICru Mircea
Plasma Phvsics. "AL L Cuza" Universitv, RO-6600, Iasi, Romania
5 December 2000 / Accepted:24 August 2001)

Abstract
Self-organization
10n1zat10n cross sectl

spatiotemporal patterns
Physics and, implicitly,
justified by recent

unded on the spatial separation of the regions where the excitation andfunctions suddenly increase is identified to be at the origin of spatial andplasma. Space-charge-limited flow and other challenging problems of Plasma
the Physics of Complexity are approached starting from a new point of view
results.

Keywords:
collective effects of e
negative differential

processes, plasma sheet, pattern formation, space-charge-limited flow,, self-organized systemplausible answers to the aforementioned challengingproblems. This scenario is grounded on collective
effects of quantum processes, related to the spatial
separation of the regions where the excitation andionization cross section functions suddenly increase.
Additionally, the presented experimental results offer a
new insight into the physical basis of the so-called
space-charge-limited flow, recently appreciated as the"most celebrated diodic event" [5].
Based on a special strategy of simulation science,
T. Sato has derived a universal rule proving that "selforganization evolves in an intermittent fashion for acontinuous excitation from an external world, while itrelaxes towards a minimum energy state in a stepwise
fashion for a sudden excitation" [6]. The self-organizing
aspects revealed in this paper represent potentially newarguments in favor of such a universal rule.

1. lntroduction
mation and instability
Basic ideas on patternmechanism in open, spatiall extended, nonlinear
not only in plasma
systems have gained special
physics but also in other fields
science [-3]. Despitein this new field ofof the collective effort. thebeing satisfactory
scientific investieation is far[2,3]. Apparently this state-of he-art is related to thetal investigations
lack of systematic experconcerning self-organization aspects observed infor the followine
different physical devices. An
science are missing [2]:important questions of nonli
are the sensitivelv
Which perturbations andmechanisms by which
controlling ones? What areof pattern formation?
small effects govern the dyn
physics at different
What are the interrelations
systems? When andlength scales in patterncontrol macroscopic
how do atomic-scale mechani

2. Experimental Results and Discussion

phenomena?

The goal of this paper i to point out that the
informational content of e scenario of selforganization already publis[4] is able to suggest*Corresponding author's e: erloz@uaic.ro

The experimental device is a plasma diode using as

02001 by The Japan Society of Plasma
Science and Nuclear Fusion Research532

Lozneanu E. et al., A New Insight into the Self-Assemblage Mechanism of complex SpaceCharge Configurations in plasmas

plasma source (PS) a negative biased heated oxidecoated filament surrounded by a grounded Ta cylinder.
The plasma created by ionization of the Ar atoms, by
the electrons accelerated towards the cylinder, diffuses
into a glass tube (5 cm inner diameter) where it isconfined by an axial magneric field (8-0.03 - 0.07 T).

A Ta-plate (2.5 cm in diameter) used as anode (A) wasplaced at 30 cm from the PS. The plasma parameters
where in the range: p = 10-4 T, fl" = (10e - l0t0) cm4, T"= (3 - 5) eV and L6 = (0.2 - 0.4) mm. In contrast with\v.

t2

the plasma diodes previously used [4], the plasma in thepresent diode is produced at lower gas pressures and isFig. 1 (a) Typical static lVcharacteristic of the plasma

confined by an axial magnetic field. This justifies somecomparisons between the present experimental results
and those recently obtained from a Q-machine plasma

the appearance and disappearance of thediode.
(b) Parts of the dynamic l(V) characteristic proving

periodical decrease of the current.

[7-9] traditionally considered collisionless [5].
The plasma column, initially in a state nearly inthermal equilibrium and asymptotic stable, is driven
away from equilibrium by connecting it to a dc power

V = V) between two conduction states of the plasma
diode before the appearance of the instability. Thus,from Fig. 1(a), we observe that the first deviation fromOhm's law appears in the voltage range Vz < V < V3

supply (external constraint). The response ofthe plasma
is emphasized in the typical static 1-Vcharacteristic [Fig.

l(a)l where V is the potential difference measured
40 Volts and, respectively,0-12 mA. This characteristic

where 1 remains nearly constant in spite of theincreasing V. Probe measurements revealed that thisanomalous behavior of the plasma column is related toreveals the presence of critical values of V, marked by

the appearance of a net negative sheet in front of A.

between PS and A. Ranges of V and l variations were 0-subscripts, for which the plasma column transits
between distinct conduction states. One of them is thespace-charge-limited flow which produces the decreaseof 1 when V = V* In the frame of the collisionless

Simultaneously performed, spectral measurements haverevealed that the cause of the sheet formation is theaccumulation of those electrons that have lost their
momentum after excitation of Ar atoms on different
levels. Since the excited Ar atoms return into the groundstate, this region appears as a luminous sheet. We notethat the formation of the net negative space charge,

plasma model this phenomenon is explained consideringa "virtual cathode" whose appearance is associated withinstabiliry [5].
For establishing the actual causes that determine
the space-charge-limited flow and the appearance oflocated at a certain distance from A, is the first
sequential step in the self-assembling of a space charge

instability, we have identified (by using modern

configuration in plasma. This process proves themethods for plasma investigation) the physical processes

presence of an atomic-scale mechanism in the formationthat explain the transition between the distinct current
conduction states of the plasma column when theapplied voltage is gradually increased [Fig. 1(a)]. The
existence of distinct conduction states proves that before
the instability appearance a series of physical processesof spatial patterns. The electrons, thermalized afterexcitations, form a net negative space charge located ata certain distance from A where the excitation crosssection function of neutrals suddenly increases.

The following important event observed in thediode is the sudden increase of 1 when V = V:. This

take place in the plasma. Their successive occurrence
creates the premises for the instability excitation. Notephenomenon indicates the appearance of a new internalthat V - Va is a critical value for which 1 abruptly
decreases and the instability spontaneously appears. The

source of charged particles. This source was identified
as a double layer (DL) whose potential-drop equals/

averaged value of1, after the instability appearance [Fig.

exceeds the ionization potential of the gas. Its presence

1(b)1, reveals the presence of a negative differential

is shown by the measured potential, electric field andresistance (NDR). The connection between the NDR
and the instability appearance is well known [5,9]. Whatis little known is the origin of the abrupt transition (forlight intensity [Fig. 2(a)]. Its appearance criticallydepends on V because its self-assembling takes placewhen the electrons accelerated towards A obtain533

Lozneanu E. el al., A New

into the Self-Assemblage Mechanism of Complex Space Charge Configurations in Plasmas

energies for which the Prod
becomes a self-enhancingof positive ionsss. Under suchconditions, the electrostatic
correlations between the twocharges, become suddenly
those forces that have initiatedprocess. This fact explains thethe space charge configuration iby a local minimum of theenhancement mechanism stoPsof the neutrals in the plasma, acting as long-range

increase of the net space

opposite net spacenant with respect toDL self-assemblingtransition of/r- (a.u.)

a state characteizedenergy [4]. The self-rAn the concentration
not allow a furtherFig. 2 Axial destribution of (a) the potential V; (b) electricfield E; (c) light intensity l, in a DLformed at 1.5
cm in front of A.

at the two sides of the

DL is self-assembling
DL. In this way a self-consi
quality
is attributed toTheself-consi
3(a)1.
tFig.
is so self-adjusting
the DL because its potential
by it produce all thethat the electrons accelera
self-maintenanceprocesses required for its conti
nt carrying plasma[4]. This is possible only in aatoms. In this state thezrrl
Fzin distance from A.
When the applied external voltage is graduallyl

decreased. the I-V character
phenomenon that indicates

ic reveals a hysteresis
existence of a voltage

DL reaches/exceeds

0.02
0.04
0.06

becomes bistable

Dista4,qefrom A(a)answers are missing [2].

after its transition into a moving phase when V>v4.

fact proving that ama diode before theis is proved in Fig. 1(b)moves away from A is illustrated in Fig. 3(b) by the
space time evolution of the profiles of the potential, ofthe electric field and of the light intensity in the plasma
column in front of the anode. This transition of the selfconsistent DL into a moving phase was identified to beat the origin of the periodic limitation of the current.
The DL motion starts when the voltage supported by theplasma column corresponds to the critical value V = V+.
The cause of this transition is a new self-enhancement

riodical decrease of 1

appears when V = V+. This i a part of the dynamic
characteristic obtained when the applied voltage islinearly increased, sufficien

fast to highlight theperiodical /-decrease when itvalue. In the static /-Va critical maximalic, where the averagedvalue of / is measured, thiswhen the circuit does notln a resrstor, and as ausual NDR when the value ofrespect to the internal resi
The transition of the initiallyresistor is high withof the plasma column.
DL into one that(b)Fig.3 (a) Sequential steps of the stable DL selfassembling process in front of A when V = Vs (Vo; (b) Temporal evolution of a DL in front of A

The space-charge-limited, the understanding
ial importance [5], isof which is considered ofrevealed in Fig. 1(a) when V V4. It appears after theistent DL when V = %.
self-assembling of the self

appearance of the instability.
where the instabilitv. i.e. the0F

generation of thelFig. 1(a)]. Note that theself-consistent DL in front of is an example of spatial
pattern formation after self.
ization. The describedexpln
the self-assembling
steps,
which
sequential
process of the self-consistentsuggest answers to thewhich. until now. theabove-mentioned questions

This is a very important ex
stable DL arises in the(ms)(hwhen the potential-drop overthe ionization potential of theDL is stable and located at arange for which the plasma

TimeFappears abruptly

process of the production of positive ions at the highpotential side of the DL when the potential drop overthe DL surpasses the value for which it is in a stablestate. The self-enhancing mechanism becomes possible534

Lozneanu E' et al.' A New Insight into the Self-Assemblage Mechanism of Complex Space Charge

because every small increase of the positive space

Configurations in plasmas

specific to self-organization [l]. The dynamic 1-V

charge in this region implies an increase of the potential

characteristic tFig. 1(b)l shows that NDR appears in thestatic 1-V characteristic only because 1 is the averaged

drop over the DL that, at its turn, determines theincrease of electron kinetic energy. Because of theenergy dependence of the ionization cross-section
function, the net positive charge at the positive side of
the DL ensures the balance between the ionization rate
and the disappearance rate of charged particles byrecombination, diffusion and so on. The moving phasevalue of the current collected by A. Since theselimitations are produced by the successive selfassemblage (storage of energy from the external power

supply) and de-aggregation (energy release in thecircuit) of DLs, these results reveal that spatiotemporal
patterns, formed by self-organization, act as the "vital"
part of systems able to generate oscillations [8,9].

starts because the net positive charge at the positive sideof the DL acts as a gas anode whose appearance
produces an increase of the electric field in front of A.

3. Gonclusions

In this way the region where electrons are accumulated

We presented experimental results able, in ouropinion, to offer a new insight into the elucidation ofchallenging problems of nonequilibrium physics [l-3].
Additionally, we revealed that the space-charge-limited

after neutral excitations shifts away from A. Because thenet positive space charge is bounded to the net negative

space charge by electrostatic forces, the whole DL
transits into the moving phase [4]. Running through theplasma column, the DL becomes able, by self-adjusting

flow, a phenomenon recently investigated in acomprehensive work [5], is physically based on: (i) theits velocity, to ensure the flux of electrons required for
its autonomous state. Evidently, this autonomy is only apartial one because a part of the flux of electrons andthe neutral concentration required for its continuous
self-assembling process is ensured by the current
flowing between PS and A. Since during the moving
phase of the DL a new DL is self-assembling in front ofA, another barrier for 1 appears in the plasma column
tFig. 3(b)1. Its development determines a decrease of 1
at a value for which the previously formed DL (which isin a moving phase) de-aggregates. During this deaggregation phase, at a certain distance from A, a bunchof positive ions is injected into the plasma column

arise, by self-organization, of a stable DL (spatialpattern); (ii) the transition ofthe stable DL into a proper,
self-sustained dynamical state (spatiotemporal pattern).

Striking phenomena observed in Nature, as for example,

the appearance of ball lightning [10] and theacceleration of charged particles by moving DLs in theaurora region ofthe Earth atmosphere [11] also could be

explained considering a self-organization mechanism
similar to that present in a plasma diode.

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3(b)1. We remark that the static I-V characteristic [Fig.

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