J. Pfasma Fusion Res. SERIES, Vol.4 (2001) 331-334

on the origin of Flicker Noise in various plasmas
LOZNEANU Erzilia*. BORCIA Caralin. pOpESCU Sebastian,SANDULOVICIU Mircea, IONITA Codrinal), DIMITRIU DanI), IGNATESCU Valerianl)and SCHRITTWIESER Romanl)
Faculty of physics, University ,,A1. I. Cuza", Iasi, Romania1)

Institute for lon physics, university of Innsbruck, Austia(Received: 5 December 2000 / Accepted: 24 August 2001)

Abstract
The current-voltage characteristic of a bounded plasma system often shows more or less strongfluctuations superimposed on the average current. Often these fluctuations are correlatedwith theformation ofcomplex space charge configurations, which in turn lead to the transport ofcharged particles
and energy through the plasma. A comparison of the fluctuation spectra obtained from (i) plasma
adiode,(ii) a high frequency plasmoid and (iii) a Q-machine shows certain similarities that could indicateacommon basis for the anomalous transport of matter and energy associated with such space charge
structures. Whereas the plasmas in a plasma diode and in a plasmoid are collisional, ae-machine plasma
is usually presumed to be collisionless. The similarities are tentatively explained by considering
a selforganization process ofthe space charge structures, which is able to successively generate double
layers.
The matter and energy stored in these double layers are transported simultaneously with
their transition
into a self-sustained propagating state.

Keywords:
self-organization, double layer, flicker noise, fireball, plasmoid,

1. Introduction
A plasma driven away from thermal equilibrium

Recent investigations in non-fusion collisional
plasmas [4] have yielded characteristic fluctuation
spectra [5-7] that are considered as a sign for self_

can perform a spontaneous transition towards a criticalstate, where an intermittent exchange of matter andorganized criticality (SOC). In such spectra, in a certain
range, the amplitude is proportional to lf (/being theenergy with the surroundings ensures a kind ofdynamical stability, which is particular to systems

frequency), wherefore we speak of lfnoise or flicker
noise. A SOC-system can be defined [g] as: (i), a
medium through which (ii) a disturbance propagates,
which causes (iii) a modification of the medium, so that

resulting from a self-organization process [l]. This selforganization process becomes possible when an extemal
constraint produces a local gradient of the kinetic energyof the electrons, which leads to a spatial separation of(iv) eventually the medium attains a critical state. after

the regions where the excitation and ionization crosswhich (v) the medium is modified no more.

section functions of neutrals maximize. Suchphenomena were observed in non-fusion collisional
plasma. They can explain the stimulation of different2. Experimental Results and Discussion
In the following we will compare the noise specraof three strongly different plasma devices: (i) a dc

kinds ofinstabilities that appear when the system is able
to perform natural oscillations [2,3].
*e_machine@2001 by The Japan Society of plasma
Science and Nuclear Fusion Research

C o rre sp onding autho r' s e -mail : erloz@ uaic. ro331

Lozneanu E. et al., On the Origin of Flicker Noise in Various Plasmas

confined between the HP and the CP. The dependence ofthe current 16p collected by the CP versus the voltage V6p
applied on the same electrode is represented in Fig' 3(b)'An important value of V for analyzing the I - V

plasma diode in which a complex space charge
configuration (CSCC) was formed, (ii) a high frequency(hf) discharge in which a plasmoid was created and (iii)a Q-machine. It is generally presumed, that the cold
alkaline plasma of a Q-machine is collisionless' and thatsuch a plasma is able to simulate experimentally someof the phenomena in magnetic fusion devices- The
presence of inelastic collisions in a low pressure plasma,
like that of a Q-machine, is not only possible but
necessary in order to explain the striking similarities
between the experimental results obtained in so different

characteristic in the plasma diode is the critical one atpoint e in Fig. l(b), where the averaged current
suddenly drops. This is due to an intermittent decrease
from a maximal value of the current, wherefore it starts
to be limited. A similar phenomenon is observed in thecase of the hf plasmoid t10l' Starting from low values of

the injected energy (proportional to the screen grid

plasma devices, like those aforementioned [3].
Moreover, the arguments for the presence of inelastic

voltage %), the current 1r, collected by the control grid'
suddenly decreases for a critical value V, (corresponding

collisions under special working conditions in a Qmachine are given in [5,9].
We start our considerations by pointing out some ofthe similarities in the initial conditions, or the causes forabsorbed by the plasmoid. This is accompanied by thetransition to an unstable phase, in which the hf field isto the point g), indicating an increase of the power

modulated by a frequency in the range of tens of kHz'As shown in Fig. 3(b), also in the Icp - Vcp characteristicof a Q-machine strong nonlinear changes of thethe appearance of flicker noise in a Q-machine, in aplasma diode and in a fusion plasma. In a fusion device
the anomalous transport of matter and energy takes
place perpendicular to the edge (and to the magnetic
field lines that confine the plasma column)' In thisregion strong temperature gradients result in strong
gradients of electron kinetic energy E"1,in' As we willelectrical conductivity of the plasma occur, shown by
the presence of critical points [9]. When the voltage
applied to the CP reaches the critical value V6p(corresponding to the point e), self-sustained oscillations
are excited in the device, resulting in a drop ofthe meanelectrode (E), respectively. In this region a strong

value of the current, in a similar way as in the plasma
diode. Moreover, the power spectra of all three signals
show lfnoise. The lfshape of these spectra could be
an indication that, in all three different plasmas,
anomalous transport of particles and energy occurs'gradient of 8"1,;nis maintained by a local acceleration ofelectrons. In all cases the anomalous transport takes
place into a direction corresponding to the gradient ofE",1;,. However, in this case the gradient of E".pin is

The intermittent modulation of the current in theplasma diode is correlated to the appearance ofpropagating DLs. These originate from the border of theshow in this paper, in a Q-machine' as well as in aplasma diode, the anomalous transport of matter andenergy has its origin in double layers (DLs) created in
front of the positively biased cold plate (CP) or

leading to flicker noise and, implicitly, to SOC'The experimental devices are schematicallypresented in Fig. 1(a), Fig. 2(a) and Fig. 3(a)CSCC that forms in front of E [1]. The anomaloustransport of matter and energy due to propagating DLs
is proved by varying the parameters of the plasma

respectively. The I-V characteristic shown in Fig. 1(b)was obtained from the plasma diode. In the case of thehf plasmoid, the dependence of the absorbed power

exceeds the value corresponding to the point e in Fig'

parallel to the magnetic field.

column bounded by the plasma source, on one side, andby the CSCC in front of E, on the other side' If V1(b), ion-acoustic oscillations in the range of tens ofkHz, excited in the plasma column, trigger a periodical
detachment of DLs from the CSCC so that the current
collected by E varies periodically. When V is further
raised, the gradient E",1,i,becomes higher' so that theversus the injected one from a Hartley oscillator aremonitored via the control grid current 1, and the screen
grid voltage V, respectively. The I, - V, characteristic
has a similar shape, as shown in Fig. 2(b). The selforganization process that explains the origin of thefrequency of the periodical DL detachment from theCSCC differs from the eigenfrequency of the plasmastrong non-linearity of the 1, - V" characteristic wasalready described in detail elsewhere [10]. Fig. 3(a)presents the Q-machine of the Institute for Ion Physics,
University of Innsbruck. In this case a Potassium plasma

column. The eigenfrequency of the plasma column is thefrequency of ion acoustic half-standing wave, which
depends on the length of the plasma column comprisedwith a densit! nr1 - 107 cm-3 was produced by surface
ionization on the hot plate (HP) and magneticallybetween the CSCC and the cathode.

itzLozneanu E. et al., On the Origin of Flicker Noise in Various plasmas
rih,$sTtBE

r0l(tt t0'(b)o ro(c) 'uu

X1.,,'" 40i'lJ,f**ri**l'i"uu

Fig. 1 (a) Schematic representation of a plasma diode; (b) /- Vcharacteristic; (c) powerspectrumof /exhibiting l/f noise.

1U:
r o'i

IU
I O':

3 l0:'0.

r0''il0 ''H^RTLEY

tarl^(c)lu00

100Frcqucrrcy ikHz)

Fig. 2 (a) Experimental device used to produce a hf plasmoid; (b) - V" characteristic; (c) power spectrum of theexternal
6
hf field exhibiting 1/f noise.
FILA,I,IFiT I{P:
€ l0''!AP{)UR BEAM

RII ror,I?LtIf l100(a)?)rr-(c)tl0frrequmt (kllZ)

Fig. 3 (a) O-machine device; (b) l"r- v", characteristic; (c) power spectrum of the ion saturation current exhibiting 1/fnoise.

Now we try to explain the behavior of the system
by assuming that it pursues a route towards chaos by
period doubling [2]. A continuous increase of Vleads toa further deviation of the frequency from the plasma

2(b)1, starting from a usual hf discharge. Firsr, theplasmoid is in an unstable state [branch cd], than it attains

column eigenfrequency and to the disappearance of thefeedback mechanism. Under such conditions the DL

a stable state [branch efl.The increase of V, determines acomparable behavior with the CSCC formed in theconfined by a DL. Its formation can only be achieved bya decrease of the screen grid voltage % [branch ab inFig.

dynamics is controlled only by internal random
fluctuations [2]. The gradient of E".y,, in front of E
determines the spatial separation of the excitation andplasma diode. The transition through a critical state [pointgl is accompanied by a decrease of 1r, indicating thepassing through a resonant state where energy is absorbed

ionization cross-section functions. Since the disruptionof the CSCC, with a frequency in the range of hundredsof Hz, is often preceded by a periodical detachment
process of the DL from the CSCC border, with afrom the internal oscillatory element of the system. This
fact can be explained by the proper dynamics of DLs,
which are periodically detaching from the surface of theplasmoid, modulating the hf field. Moreover, themodulation changes its shape with the increase of thefrequency ofhundreds ofkHz [1,3], the superposition ofthe above two processes leads to the observed llf shapeof the power spectrum, seen in Fig. l(c).

injected energy, passing through period doubling states.
Anomalous transport of particles and energy is possible
during the propagation of the DLs, in a similar way as

As already shown [0], the hf plasmoid is also
JJJ

Lozneanu E. et al., On the Origin of Flicker Noise in Various Plasmas

therein, including gradients of E",p;n towards the edge[13]. Therefore the striking similarity, emphasized inthis paper, between the power spectra observed in ourdevices and those obtained from many fusion devices

that one in a plasma diode. The power spectrum of thehigh frequency field also has 1// shape, confirming ourassumption that flicker noise is present in such devices.
For explaining the observed current jumps in the Qmachine we have invoked global effects also related tot13,141 suggests a common physical basis. Considering
the energy dependence of the excitation and ionization

the spatial separation of the regions where the neutral
excitation and ionization cross-section functions
maximize [5]. After the creation of a DL in front of CP
11,21, the transport of matter and energy is initiated by
the effect of propagating DLs. This takes place when thevoltage applied to CP reaches the critical value

cross sections for Ar [15], it results that their energetic
separation occurs at 17 eV. This value corresponds tothe order of magnitude of E",1,in obtained in bothcollisional plasmas investigated by us. For the Caltech
Tokamak plasma E",1,in 4t the edge is about 5-25 eY[16]. Because of the presence of a gradient of E",pin at
the edge of fusion plasmas a spatial separation of theregions where excitation end ionization reactions also
occurs in that region. The emission of visible light fromcertain fusion devices proves, for example, the presencecorresponding to the point e in Fig. 3(b) and an
instability well-known as potential relaxation instability[PRI in Fie.3(c)] sets on [11]. For this CP potential
value the DLs transit into a similar dynamical state asthat in a plasma diode. By their dynamics the DLstransport matter and energy accumulated in them during
their creation. After the detachment of one DL from theregion where it was generated, the conditions for thecreation of a new DL reappear. Therefore an internalof neutral excitation reactions, a necessary condition forthe creation of DLs in our model.

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