Journal of Modern Physics, 2012, 3, 943-946
http://dx.doi.org/10.4236/jmp.2012.39123 Published Online September 2012 (http://www.SciRP.org/journal/jmp)
Line Shapes in the Magnetized Plasmas
Kamel Touati-Ahmed
1*
, Mohammed-Tayeb Meftah
2
1
Lycée Professionnel Léonard de Vinci, Marseille, France
2
Department of Physics, Laboratory of Research in Plasma and Surface, University of Ouargla, Ouargla, Algeria
Email:
*
ktouati@yahoo.com
Received July 11, 2012; revised August 22, 2012; accepted August 29, 2012
ABSTRACT
Till now, the most studies of Lyman alpha line are concerned only by the Stark effect. In our knowledge few investiga-
tions are developed for the plasmas subjected to a magnetic field. In this paper we present the combined effect, Stark-
Zeeman, on the spectral line shape. The dynamic effects due to the time fluctuation of the electric microfield and the
radiation polarization are also taken into account.
Keywords: Line Profiles; Radiation Polarization; Stark Effect; Zeeman Effect
1. Introduction
In plasmas, the emitter atoms can be well represented by
the spectral line shapes. These are, combined with an
adequate theory, important tools of diagnostic of densi-
ties and temperatures in astrophysical and laboratory
plasmas as in the fusion experiences. Most of the works
on Lyman alpha lines, up to new, are only concerned the
Stark effect whereas a very little investigation has been
done on the plasmas in the presence of an external mag-
netic field (combined Stark-Zeeman effects). We observe
today a lot of plasmas where magnetic fields reign: As-
trophysics (magnetic stars, white dwarf, neutron stars),
high density energy plasma and magnetic fusion (toka-
maks, stellator, pinch). To shake off the difficulties re-
lated to the complexity of different mechanisms of the
broadening, the theory must consider nearly the interac-
tion between the emitter and all the plasma in one part
and between the emitter and the external fields, electric
and magnetic, in other part, without neglecting the inter-
nal structure of the emitter. In this work, we have pre-
sented a model of the absorption or emission lines that
relay on the distinction between the emitter atom as a
quantal system with a high number of levels and its en-
vironment in presence of a constant external magnetic
field. In presence of magnetic field, the emitted light is
polarized. In this case, the line shape depends on the ob-
servation direction and also on the electric field direction
with respect to the external magnetic field direction. This
dependency makes the calculations very difficult because,
in the presence of an external magnetic field, the hy-
pothesis of the isotropic plasma is not valid. We have
then thought to fix the direction of observation and to
consider all the possible directions of the ionic microfield
E. We have then developed in this work the general the-
ory of the broadening of the spectral line shape in the
magnetized plasmas using the framework of the time
dependent perturbations theory.
2. Transitions Probabilities
We use the time dependent perturbations theory to de-
scribe the transitions probabilities between the states α
and β which are given by [1]:
2
2
1
2π 2π
exp
e
q c
w i
mc
E E
ε P kr
ε
(1)
where m and r are the electron mass and the position op-
erator respectively, whereas P and are the polariza-
tion vector and its unit vector of the photon.
The radiation is specified by the frequency and
the wavelength vector . is the volume of the ra-
diative system and c is the light velocity. Let
k
d d f f E E
E d E E
E
the number of states whose energy is in
the infinitesimal band ; . The transition prob-
ability from the state
to a state whose energy is in
this band can be written as:
1 1
d d w w f E E
(2)
Inserting (1) in (2), we find:
2
2
1
2π 2π
d exp
e
q c
w i
mc
E E f E dE
ε P kr
(3)
*
Corresponding author.
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