J. Plasma Fusion Res. SERIES, Vol.4 (2001) 605-608

Trapping of Pellet Gloud Radiation in Thermonuclear Plasmas
SERGEEV V.YU.I*, MIROSHNIKOV I.V.l, SUDO ShigErU2, LISITSA V.S.3 ANd NAMBA C.2

lstate Technical {Jniversity, Politechnicheskaya
2National Institute

29 , st.petersburg, 195251 Russia

for Fusion science, oroshi-cho 322-6, Toki 509-5292 Japan
3Nuclear Fusion Institute
RRC "Kurchatov Institute", Kurchatov sq.46, l23tg2 Russia(Received: 5 December 2000 / Accepted: 3 September 2001)

Abstract
The experimental and theoretical data on radiation trapping in clouds of pellets injected into
thermonuclear plasmas are presented. The theoretical modeling is performed in terms of equivalent Stark
spectral line widths under condition of LTE (Sakha-Boltzman) in pellet cloud plasmas. It is shown that
adomain ofblackbody radiation could exist in hydrogen pellet clouds resulting in "pellet disappearance"
effect which is absent in a case ofimpurity pellet clouds. Reasons for this difference are discussed.

Keywords:
pellet, cloud structure, ablation, radiation, trapping, LTE

1. Introduction

clouds and to compare them with experimental

Pellet clouds are low temperature and high density

observations in thermonuclear installations.

plasma structures driven by a hot thermonuclear plasma

2. Experimental Data(see review ref. [1]). The experimental results show thatthe hydrogen pellet position in the direction across andalong magnetic field becomes undistinguishable at some

The pellet cloud intensity distributions deduced
from the fast photography measurements in T-10 [2] aredistance from the pellet surface resulting in "pelletdisappearance" effect. The effect seems to be due to ablackbody radiation which covers all the radiation
within that distance hiding the exact pellet position. The
effect exists for hydrogen and is absent for impurity (inshown in Fig. 1. Measurements have been done in thetotal visible range of lighr (400-700 nm) with exposure
times of about 7 ps for hydrogen pellet clouds shown inFig. la and 40 ps for carbon ones shown in Fig. lb.
Distributions of cloud intensities both along(longitudinal) and across (transverse) to the magnetic

particular carbon) pellet clouds.

A complete analysis of these effects requires anaccount of the pellet cloud dynamics and radiation
trapping effects self-consistently. However, there is no
reason to do it at the present state of the problem
because the pellet dynamics is not clear up to the end.
So the dynamic parameters of pellet clouds extracted

field are shown in Fig. 1. It is seen from Fig. lb that
intensities of the carbon pellet cloud have a sharp
maximum corresponding to the current pellet position inthe plasma. The striking phenomenon is an appearanceof "plateau" region of intensity in the hydrogen pellet
cloud (Fig. la). This "plateau" region has Ror = 3-4 mmfrom the dynamic theoretical models and theexperimental observations ll,2l are used below as input

in the transversal and 26 = 30-40 mm in thelongitudinal direction resulting in "pellet disappearance"
inside the domain It is supposed that this region is due
to a transition of the radiation observed into Black-Bodv

parameters for radiation trapping phenomena.

The goal of the present paper is to performtheoretical estimations for radiation trapping in pellet*Corresponding

author's e-mail: sergeev@ phtf.stu.neva.ru
605@2001 by The Japan Society of PlasmaScience and Nuclear Fusion ResearchSergeev Y . et aI., Trapping of Pellet Cloud Radiation in Thermonuclear Plasmas

transversal direction (cm)1.0012345

0.89ca)longitudinal .,-1l--......-t"EG'o.az 0.4
z o.2

I1N.

t

02

tl't

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t

hydrogen pellet cloud with a given distribution of thetotal neutral density N"1(r) in the transversal direction 'r'with I cm total cloud radius (see Fig. 1a). We consider
only domain ("plateau" region) part of the cloud taking
into account that the toroidal density distribution in thislongitudinal direction (cm)0246810longitudinulGi,

Io0III

part of the cloud is expected to be a weak function of alongitudinal co-ordinate [3]. Here, the cloud densityb);{,tr1rt
i08

temperature profiles used in simulations'

0246810j06

Fig. 2 The neutral, electron densities and electronI-.--r'\traniversal r -lvlf

10A

transversal cloud direction (cm)I,11..

|,e0.6

toroidal distribution is assumed to be uniform. Then' aof the cloud
fairly large density of N"ro = lQle"ttt-3
domain could be estimated as N"16 = N '2' Rpl(Rzry'Zg' Vo) using a pellet ablation rate value N =5.1023 atls (calculated using the conventional Parks's
scaling for T" - 900 eV and N" - 3'1013 cm-3 measured
for the minor radius position of pellet for Fig. la) andpellet velocity Vo - 5 .l0a cm/s.

transversalIIII,

012345The Sakha-Boltzman equilibrium is assumed
through all the estimations below. Validity of thistransversal direction (cm)approach was confirmed by estimations done using Ref.

[4]. The density N"1(r) and temperature I"1(r) profiles in
he cloud were varied in the model with a goal to satisfy
experimental data and estimation of N"ro presented

Fig. 1 Distributions of cloud intensities in the 400-700

nm spectral range in longitudinal (solid) andtransversal {dashed) direction for hydrogen (a)and carbon (b) pellets injected in T-10 plasmas [21.
Cloud scales are shown in horizontal axes.

above:?"r(r) = T"ro It - exp(-(r/L"r121] .
N.r(r) = N"ro exP(-(r/L.r)2)(BB) one for the hydrogen pellet cloud, A number ofHere L"1 is a characteristic decay length of the cloudparameters that is varied in simulations. The neutral andelectron density distributions together with the electron
temperature profile in the cloud are presented in Fig. 2.

experimental observations (see Ref. [1]) makes possible

to accept the following values of pellet cloudparameters: typical electron density measured using
Stark broadening ofpellet intensity lines is order of l0r7

As shown below, under such plasma conditions a strong
trapping of radiation measured in F/o and I/p spectral
lines is possible at a specific cloud radius r - Rpr.
The widths of spectral lines increase with thecm-3; electron temperature is about of 2-3 eY measured

by a ratio of line to continuum intensities with its
increase up to fcr6 - 5 eV at the pellet cloud boundary.

increase of optical depth of the media resulting in theBB radiation inside equivalent widths of these lines [4].

3. ModelingTo make a model consistent with the experimental
observations mentioned above, let us consider aMoreover, the equivalent widths of these lines can606sergeev Y ' et al', Trapping of pellet cloud

overlap in the domain to approach a BB radiation

Radiation in Thermonuclear plasmas

in thetotal spectral range observed. The main mechanismv,responsible for the spectral line broadening in thecloudis the Stark effect in the electric fields of cloud plasma'ctions. Note that the static line shape can be assumed'ocompletely re-distributed over frequencies duetothermal motion of ions t5l. The equivalent width
Aar"ofor static line shapes in the far wings of spectral lines
was estimated for large values of optical depth z
as10"
equivalent widthta

ch1.0'nStarkwidth

F 10"

()

Fl
1.0t'

0follows [4]:

0.2

0.4

0.6

0.8

transversal cloud direction (cm)La.- 1.5 .Ao5 ?). ras ,L,ror- 2.6. C. U7z, tr= Kst,
where C is the Stark constant of the spectral lines
observed, re is the absorption coefficient dependingon
the population of the lower atomic level, a line widthand atomic parameters of the transitions (see Ref.
t6l).
The dependence ofthe equivalent width of116 _line
on the cloud radius .r, is shown in Fig. 3. One canseethat the equivalent width more dominates over theStark

one when approaching the central parts of the pellet
cloud whereas the conventional Stark broadening takes
place at the cloud periphery. The radiation intensity
outgoing from the optically thick pellet plasma in theFig. 3 Comparison of the equivalent andStark width ofH, line at different radii inside the pellet cloud.

=GIrA!).A

tro

transversal cloud direction (cm)400-700 nm spectral range is shown in Fig. 4. It is seenFig. 4 Comparison of the pellet cloud and BB radiationthat the cloud radiation reaches that ofthe BB one nearintensity profiles in the 4OO_700 nm spectrala specific cloud radius r = 0.27 cm that is consistent
with Rpr evaluations from Fig. la.

range.

The main difference between hydrogen andimpurity pellet clouds is that the oscillator strengths arelocalized in two (or three) spectral lines for hydrogenof radiation trapping inside pellet clouds. Due to therough approach both for density and temperature
distributions inside clouds as well as due to theand are distributed over the observed spectral range forimpurities. This results in the quadratic Stark effect forimpurities in contrast with the linear one for hydrogenas well as in different values of absorption coefficients.

simplified radiation trapping model used for strongly
overlapping spectral lines, there are some uncertainties

One must take into account also the difference in neutralin simulated parameters of the problem. However, thepresented model seems to be consistent withthedensities for both cases due to a difference in the pellet
ablation rates together with a difference of ionization
potentials in Sakha-Boltzman equilibriums.

experimental observations available. The measuremenrsof electron densities of pellet clouds are consistent withthe simulated values -1017 cm-3 of electron density inthe pellet cloud periphery where the equivalent widthisclose to conditional Stark one (Fig. 3). The temperature

Such estimations show that the equivalent opticalwidths for the hydrogen cloud are more than one orderof magnitude larger than impurity ones. Therefore, whenhydrogen lines are overlapped to create black bodyradiation, the impurity lines are still non_overlapped.
This is a possible reason for existence of the ..pellet
disappearance" effect for hydrogen pellets and it,sabsence for carbon pellets.

measurements seem to belong to the cloud domain neartransformation of the intensity to the BB one (Fig. 4)
where the temperature is near 2_3 ey (Fig. 3). At thesame time the possibility of BB parts of the pellet

clouds radiation is also consistent with ..pellet
disappearance" effect discussed above. The cloud

4. Discussion

parameters for these effects are not so far fromThe consideration done above claims a possibility

usually accepted for pellets.
607the ones

Sergeev V. et al., Ttapp\ngof Pellet Cloud Radiation

Acknowledgments
This work was supported by the JSPS (Japan) grant
ID No. L00537.

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