Some Macroscopic Properties of Plasma State through Thermodynamical Approach

M.S.Yaghmaee a, Kh.Alavi b, B.Shokri c,*
Plasma Group, Laser-Plasma Research Institute, SBU, Teh. Iran
a, c, * correspondent author
Abstract. In many plasma applications when we wish to make a material modeling of either plasma state or the products
(macro-state formalism), we would expect to use some macroscopical measurable materials properties which describe the
micro-state of plasma, in other word the science of thermodynamics and materials. But there is still a huge gap between
these two fundamental sciences and the plasma science. One of the main aims for any experimental or theoretical
investigating would be to find how our material “system” behaves. For the plasma state when we try to use simple
algorithms of thermodynamics of materials science, we face with a gap of interface between the plasma and material
science, either in terminology or in understanding the problem itself. For starting to get such new approach to the problems,
here we focused on the time period before the plasma gets into temperature equilibrium. So, we try to combine the classical
hypothesis somehow applicable in that plasma state, although the introduction of time and change of physico-chemical
property by time itself means a great challenge. Such process yet leads to some global and general hypothesis but the first
step towards any further experiments or exact material modeling of plasma. Here we focus on some state equation for
mixing of different particles with different temperatures, temperature relaxation, interaction pressure during the relaxation,
activity of interaction, excess Gibbs energy of interaction, heat capacity of interaction and similar questions.
Keywords: macroscopic and microscopic properties, micro- macro- state, thermodynamical modeling, plasma state, excess
energy, interaction pressure, relaxation
PACS: 51.30.+i, 52.25.Kn, 64.10.+h, 67.40.Kh,
By micro- and macro-states we mean correspondingly the physico-chemical behaviors of particles in the system
determined by their own interactions, and the physico-chemical behaviors of system globally which contains an overall
effect of micro-states too. Thus, any macro-scale model or properties included the micro-states of particles too.
Therefore, we need such micro and macro quantities to say something about the state of system, extensive properties like
T, p,…, and even if micro states are known we have fundamental formalism for estimation of partial E, p, G, …, do
simulation and make indirectly modeling applications. Then, here we expect to reach some equation of state under
restricted classical thermodynamical conditions “EOS”, or a quasi-thermodynamical state “QEOS” or even a kinetic
equation of state “TKEOS”. From the time scaling the problem, the system starts from TKEOS where particles with
different temperatures and pressures start interacting and then through QEOS state where still some reactions occur
without net chemical change the system reaches a total EOS state. Let us first discuss basic assumption on extensive
properties in our system; -volume; we may suppose a constant volume for plasma just for sake of simplicity or regarding
the fact that for such interaction ionized gas like state which has time dependency in temperature and pressure of each set
of particles, we need to have at least volume quantity to be fixed even for a short quasi-equilibrium time scale. –
temperature; in such kinetically changing system each sets of particles may have their own values and during TKEOS
stage system goes through a temperature relaxation which in a simple form for example it may have an exponential form.
-number of Moles; we have different particles with different number of moles, but as we do not consider any net
chemical reaction yet, here the values of moles remain constant. -pressure; as the temperatures could be different for
each set of particles, and consequently as no net mass change occur, particles should have different pressures for each set
of particles as partial values. Further on since pressure is an additive physical quantity and since we try to write the
behavior of system in micro-scale, we focus of partial terms. Regarding all terms of partial pressures for a particular
particle set we may write,

The first term respectively shows the kinetically pressure and has the form in Eq(2), Concerning the external
fields, except magnetic other fields have no net forces exerting on neutral or charged spices in plasma to produce extra
pressure, but as magnetic field has a constant force which is neither depends on number of spices or time of process, then
the pseudo-kinetics process “studied here” will not be affected by this pressure, so its partial terms will be
correspondingly omitted, then,

-combination and Interrelations; if we suppose there is no chemical reaction between particles for changing the
number of moles at least in net values, then the temperature and pressure directly relate to each other and play the main
role during the three stages of state namely: TKEOS, QEOS and EOS and dominate the whole macroscopical behavior
and obviously contains all micro-states inside themselves.

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