S-R4-1
Underlying physics of plasma production and ionization process
趣旨説明、プラズマ生成・電離過程の奥に潜むもの
Yasuaki Kishimoto
岸本 泰明
Graduate School of Energy Science, Kyoto University, Uji, Kyoto 611-0011, Japan
京都大学大学院エネルギー科学研究科 〒611-0011 京都府宇治市五ヶ庄
All plasmas are produced from neutral medium via complex atomic and molecular processes. During such
discharge processes, many types of prominent spatio-temporal dynamics and structures are revealed, e.g.
sudden change of the state, avalanche dynamics, fine branched structures, etc., which are seen to beprobabilistic and non-diffusive. From advanced simulations and models including atomic processes, andalso experimental observations using ultra-fast diagnostic techniques, those processed are found to beunderstood by the percolation transition and associated critical phenomena. We present simulations/models,and experimental observations and studies the underlying physics processes of discharges.

1.

Introduction
Plasma production and ionization processes,
where discharges and lightning are typicalexamples, are complex exhibiting prominent spatiotemporal structures [1]. The sudden trigger of theevent followed by the avalanche dynamics andemergence of complex fine branched structures are
the universal nature, which remind us that theprocess is probabilistic so that they are hardlypredicted and controlled. The change of the state inneutral medium (solid, liquid, gas) has beensuccessfully described as phase transition under theassumption of the thermodynamics equilibrium.
However, no formal theory exists regarding theplasma production as one of the phase transition.
This may be partially due to the fact that theionization process which consists not only ofvarious kinds of particle (atoms and molecules,
charged macro- particles, multiple changed ions,electrons etc.), but also of various kinds ofelectromagnetic fluctuations. Namely, the existing
concept is not simply introduced and a newparadigm is necessary.
In order to understand such complex discharged
process, we explored theoretical and computationalmodels which include various atomic processes indescribing complex non-equilibrium and nonstationary ionization processes [2,3], diagnostic
techniques in discharge experiments available forthe observations of complex spatio-temporaldynamics and structures. Specifically, from thesimulation studies, we have reached an idea that thedischarge process exhibits a percolation dynamics
where probabilistic process characterized by acritical parameter plays an essential role. We also
found that the process can be classified into threefundamental processes with different time andspatial scales as discussed in Sec.2. which leads us

a guiding principle in understandings the complex
discharge phenomena. We found that the non-local
process associated with plasma kinetics such as
runaway particles play an important role.
2. Discharge kinetic simulation
In order to elucidate the complex ionization
process, we explored an extended particle based
integrated simulation code, EPIC3D, which
includes various atomic processes and collisional
relaxation processes. Using the code, we performed
a discharge simulation for a high pressure neon gas
with the density of 4.6x1020cm-3, where the electricfield of E=107V/cm is uniformly applied in thesystem. A tiny ionization spot with Ne+2 is set
initially to trigger the discharge.
Figures 1 shows the dynamics of ion charge
density at 40, 44 and 45psec, respectively. Note thatno significant events happen up to 40psec (a), but
after a few psec later, i.e. 44psec (b), a streamer likestructure is triggered suddenly across the wholesystem, followed by micro-scale branching leading
to a global net-like structure during 1 psec, i.e.
45psec (c). Figure 2(d) illustrates the spatial
distribution of the ion charge state at 40psec before
the sudden branching takes place, i.e. t=42psec (b).
Many tiny ionization spots are found to be emergedin the entire system. When the number of spots (orequivalently “packing fraction” of the spot) exceeds
a certain critical value, micro-scale discharges are
triggered among neighboring spots. Such many
local branching events propagate leading to an
explosive dynamics over the wide reagion. Such a
process is similar to that of forest burning modeledby the percolation theory, which exhibits thecharacteristics of critical phenomena.
The generation of many ionization spots which
distributes over the system results from runawayelectrons with long mean free path due to theapplied high voltage. Similar process has been
discussed as the origin of lightning. A Monte Carlosimulation of the generation of energetic particles(runaway electrons, positrons, photons etc) andtheir cascading is shown in Fig.2 [4], leading tosimilar ionization spots.
3. Classification into three elementary processes
From the evidences discussed in sec.2, we haveclassified the sudden explosive event into threefundamental physical processes :① the formation of initial condition,②the trigger and chain reaction,③subsequent global structure evolution andpattern formation,
which provide a guiding principle in understanding
the complex discharge phenomena. Namely, it canbe seen that the global and sudden discharge evens
result from the organic connection of theseprocesses. Specifically, the item ①, where nonlocal dynamics of particles and electromagnetic
fluctuations play essential roles, is an importantingredient, which is referred to as the science ofinitial state. The dynamics of Figs 1 (a), (b), (c)correspond to ① , ② , ③ ,respectively. Note thatthese ingredients have a similarity to those ofpercolation and related critical phenomena.
4. Experiments observation and percolation
dynamics and modeling
We have performed various experiments andalso explored a theoretical modeling based on theclassification in Sec.3 in subsequent discussions.
In S-R4-2[5], the branching condition andtemporal streamer evolution are investigated using
ultra-fast ICCD camera (corresponds to ② and③). Specifically, the laser induced density and/or
field fluctuations are found to be a factor intriggering the streamer initiation (① and ②). In
S-R4-3, the underwater pulsed discharge
experiments are arranged to clarify the trigger
mechanism of the streamer and its evolution. Thechange of the state prior to the initiation of thedischarge is observed for the first time (①), whichis consider to originate from the change ofreflective (dielectric) constant. In S-R4-4, highvoltage impulse discharges in air initiated by laser
are investigated. Runaway electrons, which areconsidered to play an important role triggering
subsequent discharges, are found to be produced
and the source is identified (① and ②). In S-R4-5,
a model based on the percolation theory including
ionization and recombination processes is presented.

The sudden structure formation is successfullyreproduced. The wide class of morphology inexperiments is found to be explained by this modelsuggesting the percolation transition capture
essential feature of discharges.
4. Summary
Complex discharge processes were investigatedcomputationally, theoretically and experimentally.
The process is found to show a similar nature as thepercolation transition which exhibits criticalphenomena. The process is classified into threefundamental processes, which leads to a guiding
principle in understanding discharges.

Fig.1 Ion charge density from EPIC3D simulation ofdischarge of compressed neon gas at three time scales [1,2]Fig.2 Transition phenomena from neutral fluid to plasmas
and classification into three fundamental processes [2-7]References[1] Y. Kishimoto, Jounal of Plasma and fusion
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