Doppler effect at the electron cyclotron and spin resonances and its applications for plasma diagnostics and electron polarization in a warm beam
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| Опубліковано в: : | Вопросы атомной науки и техники |
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| Дата: | 2000 |
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| Формат: | Стаття |
| Мова: | Англійська |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2000
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| Цитувати: | Doppler effect at the electron cyclotron and spin resonances and its applications for plasma diagnostics and electron polarization in a warm beam / B.I. Ivanov // Вопросы атомной науки и техники. — 2000. — № 6. — С. 183-184. — Бібліогр.: 5 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859713782648930304 |
|---|---|
| author | Ivanov, B.I. |
| author_facet | Ivanov, B.I. |
| citation_txt | Doppler effect at the electron cyclotron and spin resonances and its applications for plasma diagnostics and electron polarization in a warm beam / B.I. Ivanov // Вопросы атомной науки и техники. — 2000. — № 6. — С. 183-184. — Бібліогр.: 5 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| first_indexed | 2025-12-01T07:06:38Z |
| format | Article |
| fulltext |
Problems of Atomic Science and Technology. 2000. № 6. Series: Plasma Physics (6). p. 183-184 183
UDC 533.9
DOPPLER EFFECT AT THE ELECTRON CYCLOTRON AND SPIN
RESONANCES AND ITS APPLICATIONS FOR PLASMA DIAGNOSTICS
AND ELECTRON POLARIZATION IN A WARM BEAM
B.I. Ivanov
National Science Center “Kharkov Institute of Physics and Technology”,
Kharkov, 61108, Ukraine (E-mail: ivanovbi@kipt.kharkov.ua)
In the Ref.[1] it is considered the method of electron
polarization using the Doppler effect at the electron spin
resonance (ESR), in the case of the monoenergetic
electron beam. In this work the development of the
method is discussed for the warm beam, i.e., for the
kinetic case instead of the hydrodynamic one.
In the analogous case, the electron cyclotron
resonance (ECR) was applied for measuring the electron
longitudinal velocity distribution [2-4]. To see the
analogy in details, let us consider a connection between
the electron longitudinal velocity distribution function
)( zvf and the curve of the cyclotron absorption of an
electromagnetic wave in a plasma, )( cP ω−ω , which
represents the dependence of the wave power (after
passing through the plasma) versus the frequency shift
near the ECR. The calculations were based on the
expression that describes the power transference from
the electromagnetic wave to the electron at the
resonance electron cyclotron frequency:
22
0
22 1
2 −τ+ω−ω′τ
=
)( c
a
a m
Ee
p , (1)
where Ea is the electric field intensity amplitude of the
right hand circularly polarized wave, 0cω is the electron
cyclotron frequency ( mceHc /=ω 0 ),
zcz vkvk 303 ±ω=±ω=ω′ is the Doppler–shifted
frequency of the wave, e and m are the electron charge
and mass, τ is the electron time of flight through the
pumping area. It is supposed here that except of τ
another factors of the ECR broadening are negligible.
For a given frequency difference 0cω−ω=ω∆ the
resonance electrons are those with longitudinal
velocities in the interval between vr and vr±∆vr, where
τ=∆
ω−ω
±= 3
3
0 1 kv
k
v r
c
r /, (2)
The ESR has the analogous contour (e.g., see[5]):
])()/[()(/ 22
1
22
10
−τ+γ+ω−ω′γ= HHPP s , (3)
where P is the mean power going from the wave to the
electron spin and back, ω′ is the Doppler-shifted wave
frequency, γ is the gyromagnetic ratio, H1 is the
magnetic field intensity amplitude of the right hand
circularly polarized wave, τ is the electron time of
flight through the pumping area, ωs is the frequency of
the electron spin resonance (ESR):
ls mcaeH γ+=ω /)(1 , were e and m are the charge
and mass of electron, c is the light velocity, lγ is the
Lorentz factor, a is the anomalous part of the electron
magnetic moment (a≅ 0.001).. (The parameters
1
1
−τωωγ )(,/ ssH can be of order 10-4 – 10-5). It is
supposed that another factors of the ESR broadening are
negligible. The probabilities of the electron spin flip due
to the quantum absorption or induced radiation are equal
one to another and are determined by the following
expression [5] (with account of vL /=τ , where L is
the pumping section length, v is the velocity of the
resonance electron):
))()((sin
)()(
)(
)(
2
1
22
22
1
2
2
12
2
Ht
H
H
tc
s
s
γ+ω−ω′
×
τ+γ+ω−ω′
γ
=
−
(4)
or by its quantum analog [5]. At the conditions
′ =ω ωs and γ π τH1 = / (because sin2(...)=1, and
22
1
−τ>>γ )( H ) we have 12 ≈)(tc , that is, the
probability of an electron spin flip is about 1 to the
moment of its exit out of a section.
The half-width of the both resonances can be much
smaller than the frequency Doppler shift:
τ/1 or effν are zvk3<< , (5)
where effν is the frequency half-width of the cyclotron
resonance for a single electron with velocity vz. In the
general case, effν denotes the frequency with which the
ω ′/ Ω
1.110.90.8
P
(a
. u
.)
8
7
6
5
4
3
2
1
0
Fig.1.
wave phase shifts in relation to the electron rotation (by
collisions, non-homogeneous, etc.). This situation is
shown in the Fig.1, where the wide curve represents a
warm plasma or dispersed beam (the Gauss contour),
184
and the narrow curve does the Lorentz contour of the
ECR (or ESR) resonance.
In this condition, the cyclotron loss is governed
primarily by resonance electrons in case of the ECR,
and the electron spin flip is realized primarily for
resonance electrons in case of the ESR.
By changing the electron cyclotron frequency as a
parameter, we can systematically measure the entire
electron longitudinal velocity distribution. In the case of
effν << τ/1 the microwave power absorbed per unit
volume has the form:
∫
+∞
∞− ω−ω
ω−ω−
= z
cz
c
z
a
a dv
kLv
kL
vf
m
Ee
P
2
03
03
22 1
2 ))((
))((cos
)(
!
!
(6)
Here L is the longitudinal dimension of the interaction
region, the “ ! ” signs correspond to the cases in which
the electron and wave are moving in same and opposite
directions, respectively.
In the case of effν >> τ/1 the microwave power
absorbed per unit volume has the form:
[ ]∫
+∞
∞− ν+ω−ω
ν
= z
effzc
eff
z
a
a dv
vk
vf
m
Ee
P
22
30
22
2 )(
)(
!
(7)
With account of (5), the integrals in the formulae
(6) and (7) take the form:
∫
+∞
∞−
π=−δπ
)()()( rrrzz vf
k
dvvvvf
k 33
(8)
The wave damping in the plasma is obtained the
form
π
−=
8
2
a
a
E
dt
dP (9)
As a result, with account of (5)-(9), the distribution
function is determined as follows:
)(
ln)(
ω∆π
ω=
P
P
Le
mvf r
0
224
, (10)
where P0 and )( ω∆P represent the wave power at
input and output of the plasma.
Let us turn now to the specific RF cavity version of
the method of determining f(vz). It is assumed that the
microwave power of a wave transmitted through a
plasma (or beam) filled the cavity is measured as a
function of the magnetic field, i.e., that P(H) is
measured. For the H11q mode of the cavity it was
received [3] the expression:
−
π
ω
= 1
240 0
0
22
3
P
P
Qe
Vkm
vf R
r
.
)( , (11)
where Vr is the cavity volume, Q0 is the cavity quality
factor, P0 is the transmitted RF power far from
gyroresonance, P=P(H) is the same but near the
resonance.
As an example, in the Fig.2 it is presented the
comparison of electron velocity distribution
measurements in the initial stage of the beam-plasma
discharge, by this microwave method and the retarding
potential method [5]. The oscillograms (left) present the
experimental P(H) curve used to calculate with the
equation (10) the curve f(vz) (middle), and the
oscillograms (right) do the distribution function
f(mvz
2/2) obtained by the retarding potential method. As
one can see, both methods give like results.
By the same way, scanning step by step the electron
spin precession frequency (e.g., by changing the
longitudinal magnetic field) and using for every step the
microwave pumping procedure described in Ref.[1], one
can polarize the electron beam in the case of the
dispersed (warm) electron beam.
References
1. B.I. Ivanov, Polarization of Charged Particles in
Monoenergetic Beams and Application in Fusion
Researches, this issue.
2. B.I. Ivanov, Proc.of the Intern. Summer School on
the Phys. of Ionized Gases, Herzegnovi,
Yugoslavia, 1970, pp. 653-677.
3. D.V. Gorozhanin, B.I. Ivanov, V.P. Prishchepov,
Zh. Tekh. Fiz., 1975, V.45, p.41 [Sov. Phys. Tech.
Phys., 1975, V.20, No.1, p.24].
4. D.V. Gorozhanin, B.I. Ivanov, V.P. Prishchepov,
Nuclear Fusion, 1974, V.14, No.4, p.493.
5. W. Louisell, Radiation and Noise in Quantum
Electronics, Ch.5, McGrow-Hill Book Co., 1964.
Fig. 2. Comparison of electron velocity distribution measurements
References
|
| id | nasplib_isofts_kiev_ua-123456789-78547 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-01T07:06:38Z |
| publishDate | 2000 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Ivanov, B.I. 2015-03-18T18:46:27Z 2015-03-18T18:46:27Z 2000 Doppler effect at the electron cyclotron and spin resonances and its applications for plasma diagnostics and electron polarization in a warm beam / B.I. Ivanov // Вопросы атомной науки и техники. — 2000. — № 6. — С. 183-184. — Бібліогр.: 5 назв. — англ. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/78547 533.9 en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Plasma diagnostics Doppler effect at the electron cyclotron and spin resonances and its applications for plasma diagnostics and electron polarization in a warm beam Article published earlier |
| spellingShingle | Doppler effect at the electron cyclotron and spin resonances and its applications for plasma diagnostics and electron polarization in a warm beam Ivanov, B.I. Plasma diagnostics |
| title | Doppler effect at the electron cyclotron and spin resonances and its applications for plasma diagnostics and electron polarization in a warm beam |
| title_full | Doppler effect at the electron cyclotron and spin resonances and its applications for plasma diagnostics and electron polarization in a warm beam |
| title_fullStr | Doppler effect at the electron cyclotron and spin resonances and its applications for plasma diagnostics and electron polarization in a warm beam |
| title_full_unstemmed | Doppler effect at the electron cyclotron and spin resonances and its applications for plasma diagnostics and electron polarization in a warm beam |
| title_short | Doppler effect at the electron cyclotron and spin resonances and its applications for plasma diagnostics and electron polarization in a warm beam |
| title_sort | doppler effect at the electron cyclotron and spin resonances and its applications for plasma diagnostics and electron polarization in a warm beam |
| topic | Plasma diagnostics |
| topic_facet | Plasma diagnostics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/78547 |
| work_keys_str_mv | AT ivanovbi dopplereffectattheelectroncyclotronandspinresonancesanditsapplicationsforplasmadiagnosticsandelectronpolarizationinawarmbeam |