EXCITATION TEMPERATURE OF A RAPIDLY VARYING PLASMA

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EXCITATION TEMPERATURE OF A RAPIDLY VARYING PLASMA

M. Numano, H. Onishi

To cite this version:

M. Numano, H. Onishi. EXCITATION TEMPERATURE OF A RAPIDLY VARYING PLASMA.

Journal de Physique Colloques, 1979, 40 (C7), pp.C7-49-C7-50. �10.1051/jphyscol:1979724�. �jpa- 00219223�

JOURNAL DE PHYSIQUE CoZZoque C7, suppZ6ment au n07, Tome 40, JuiZZet 1979, ,page C7- 49

EXCITATION TEMPERATURE ff A RAPIDLY VARYING PLASMA

M. Numano and H. Onishi

'.

CoZZege of Engineering, University of Osaka Prefecture, Sakai, Japan.

%itsubishi Atomic Power Industries, Inc., Tokyo, Japan.

As is well-known, the excitation tem- perature, which is determined from the pop- ulation distribution of excited atoms in a plasma, is not always equal to the electron temperature related to the thermal motion of electrons. The discrepancy between these two temperatures is caused by vari- ous effects /1,2,3/. Recently, it was re- ported that, i.n an expanding jet of plasma, the electron density decreases quite rapid- ly along the flow and that the excitation temperature differs markedly from the elec- tron temperature / 4 / . When the variation of the electron density is too rapid for the population of the excited atoms to fol- low, the plasma may not remain in thermal equilibrium, resulting in the difference of the excitation temperature from the elecc tron temperature.

In this report the influence of elec- tron-density variation on the excitation temperature will be investigated. For this purpose, it is necessary to examine the variation of the population distribution of excited atoms, when the electron-density variation is given as a function of time.

Here we shall consider a hydrogen plasma, and the density of atoms N in the excited state p is assumed to be described by P

where Ne is the electron density. The co- efficient K(p,q) is the rate of collision- a1 transition from state p to state q, K(p,c) is the electron impact ionization rate from state p, and K(c,p) is the colli- sional recombination rate to state p.

These coefficients are evaluated from Drawin's formulae for the cross sections of excitation and ionization due to elec- tron collisions / 5 / and the principle of detailed balance. The results are in good agreement with those of Kunc and Zgorzelski 6 The radiative recombination coeffi- cient P(p) to state p is evaluated from the well-known photo-ionization cross section and the Milne relation / 7 / . The sponta- neous transition probability A ( p , q ) is found in reference 8.

Now let us consider a plasma which is in equilibrium for t < ^{0. At t = 0, the}

electron density begins to decrease expo- nentially with time as

where Ne(0) is the initial electron densi- ty and to is the decay-time constant of the electron density. The electron temperature Te is assumed to remain constant.

A few results of the numerical calcu- lations are shown in in Figs. 1-4. In these figures the population distribution and the excitation temperature are plotted against the ionization energy of excited states at the time t = to for Ne(0) = 10 14 cm-3 and to = 0.01, 0.1 and 1 ps. The ex- citation temperature Tex was determined

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979724

from the Boltzmann plot by REFERENCES

l/Tex = k

-

where k is the Boltzmann constant and g is 2. M.Numano et al., JQSRT

15,

P

the statistical weight of state p. The ^3. M.Numano, JQSRT

20,

electron temperature was taken to be 5000K 4. M.Abe, MS Thesis, Kyoto Univ. (1977).

in Figs. 1 and 2 and lOOOOK in Figs. 3 and 5. H.W.Drawin, Report EUR-CEA-FC-383

4. (1966).

From these results it may be concluded 6. J.Kunc and M.Zgorzelski, At. Data nucl.

that except for extremely highly excited Data Tab.

15,

states the excitation temperature is much 7. D.R.Bates and A.Dalgarno, Atomic and lower than the electron temperature. Molecular Processes (Ed. by D.R.Bates),

Academic Press, New York (1962).

8. W.L.Wiese et al., Atomic Transition Probabilities, Vol.1: Hydrogen through Neon, NBS, Washington,D.C. (1966).

-

W 0 1

Ionization energy (eV) Fig. 1 Excitation temperature for Te =

5000K and Ne(0) = 1014 ~ m - ~ .

u

w Ionization energy (eV) Fig. 3 Excitation temperature for T =

lOOOOK and Ne(0) = 1014 cme3f

'C,'

.d lo3 .Z 102-

F: d

I ?

P k

cd

e

" 102 - ^U

a a

M

a 0 1 1

Ionization energy (eV) Ionization energy (eV)

Fig. 2 Population distribution of excited ~ i 4 population distribution ~ . of excited atoms for Te = 5000K and Ne(0) = atoms for Te = lOOOOK and N,(O) =

10l4 cm-3. 1014