The effect of low-density background plasma on frequency and energy characterictics of coaxial gyrotron cavity
The effect of low density background plasma on the electromagnetic field energy density in the ITER relevant coaxial gyrotron cavity is studied. The model of cold collisionless magnitoactive plasma is used. The dispersion relation and expression for the density of RF energy in plasma-filled coaxial...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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| Цитувати: | The effect of low-density background plasma on frequency and energy characterictics of coaxial gyrotron cavity / Yu.K. Moskvitina, G.I. Zaginaylov, V.I. Tkachenko // Вопросы атомной науки и техники. — 2012. — № 6. — С. 31-33. — Бібліогр.: 5 назв. — англ. |
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irk-123456789-1090942016-11-21T03:02:31Z The effect of low-density background plasma on frequency and energy characterictics of coaxial gyrotron cavity Moskvitina, Yu.K. Zaginaylov, G.I. Tkachenko, V.I. Магнитное удержание The effect of low density background plasma on the electromagnetic field energy density in the ITER relevant coaxial gyrotron cavity is studied. The model of cold collisionless magnitoactive plasma is used. The dispersion relation and expression for the density of RF energy in plasma-filled coaxial gyrotron cavity are derived in the analytical form and analyzed numerically. It is shown that presence of low density plasma in coaxial gyrotron cavity leads to downshift of the operational frequency and to decreasing Ohmic loads of both the outer and inner conductors of coaxial gyrotron cavity. Изучено влияние фоновой плазмы низкой плотности на плотность энергии электромагнитного поля в коаксиальном резонаторе гиротрона ITER. Используется модель бесстолкновительной, магнитоактивной плазмы. Дисперсионное соотношение и выражение для плотности СВЧ-энергии в плазмонаполненном коаксиальном резонаторе гиротрона получены аналитически и исследованы численно. Показано, что наличие плазмы низкой плотности в коаксиальном резонаторе гиротрона приводит к уменьшению рабочей частоты и уменьшению омических потерь на внешней стенке и внутреннем проводнике резонатора коаксиального гиротрона. Вивчено вплив фонової плазми низької щільності на густину енергії електромагнітного поля в коаксіальному резонаторі гіротрона ITER. Використовується модель беззіткненної, магнітоактивної плазми. Дисперсійні співвідношення та вираз для густини НВЧ-енергії в плазмонаповненому коаксіальному резонаторі гіротрона отримані аналітично та досліджені чисельно. Показано, що наявність плазми малої густини в коаксіальному резонаторі гіротрона призводить до зменшення робочої частоти та зменшення омічних втрат на зовнішній стінці та на внутрішньому провіднику резонатора коаксіального гіротрона. 2012 Article The effect of low-density background plasma on frequency and energy characterictics of coaxial gyrotron cavity / Yu.K. Moskvitina, G.I. Zaginaylov, V.I. Tkachenko // Вопросы атомной науки и техники. — 2012. — № 6. — С. 31-33. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS: 52.35.Hr, 84.40.Ik http://dspace.nbuv.gov.ua/handle/123456789/109094 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Магнитное удержание Магнитное удержание |
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Магнитное удержание Магнитное удержание Moskvitina, Yu.K. Zaginaylov, G.I. Tkachenko, V.I. The effect of low-density background plasma on frequency and energy characterictics of coaxial gyrotron cavity Вопросы атомной науки и техники |
| description |
The effect of low density background plasma on the electromagnetic field energy density in the ITER relevant coaxial gyrotron cavity is studied. The model of cold collisionless magnitoactive plasma is used. The dispersion relation and expression for the density of RF energy in plasma-filled coaxial gyrotron cavity are derived in the analytical form and analyzed numerically. It is shown that presence of low density plasma in coaxial gyrotron cavity leads to downshift of the operational frequency and to decreasing Ohmic loads of both the outer and inner conductors of coaxial gyrotron cavity. |
| format |
Article |
| author |
Moskvitina, Yu.K. Zaginaylov, G.I. Tkachenko, V.I. |
| author_facet |
Moskvitina, Yu.K. Zaginaylov, G.I. Tkachenko, V.I. |
| author_sort |
Moskvitina, Yu.K. |
| title |
The effect of low-density background plasma on frequency and energy characterictics of coaxial gyrotron cavity |
| title_short |
The effect of low-density background plasma on frequency and energy characterictics of coaxial gyrotron cavity |
| title_full |
The effect of low-density background plasma on frequency and energy characterictics of coaxial gyrotron cavity |
| title_fullStr |
The effect of low-density background plasma on frequency and energy characterictics of coaxial gyrotron cavity |
| title_full_unstemmed |
The effect of low-density background plasma on frequency and energy characterictics of coaxial gyrotron cavity |
| title_sort |
effect of low-density background plasma on frequency and energy characterictics of coaxial gyrotron cavity |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2012 |
| topic_facet |
Магнитное удержание |
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http://dspace.nbuv.gov.ua/handle/123456789/109094 |
| citation_txt |
The effect of low-density background plasma on frequency and energy characterictics of coaxial gyrotron cavity / Yu.K. Moskvitina, G.I. Zaginaylov, V.I. Tkachenko // Вопросы атомной науки и техники. — 2012. — № 6. — С. 31-33. — Бібліогр.: 5 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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1837029261071876096 |
| fulltext |
ISSN 1562-6016. ВАНТ. 2012. №6(82) 31
THE EFFECT OF LOW-DENSITY BACKGROUND PLASMA ON
FREQUENCY AND ENERGY CHARACTERICTICS OF COAXIAL
GYROTRON CAVITY
Yu.K. Moskvitina1,2, G.I. Zaginaylov1,2, V.I Tkachenko1,2
1NSC “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine;
2V.N. Karazin Kharkov National University, Kharkov, Ukraine
E-mail: Yu.Moskvitina@gmail.com
The effect of low density background plasma on the electromagnetic field energy density in the ITER relevant
coaxial gyrotron cavity is studied. The model of cold collisionless magnitoactive plasma is used. The dispersion
relation and expression for the density of RF energy in plasma-filled coaxial gyrotron cavity are derived in the ana-
lytical form and analyzed numerically. It is shown that presence of low density plasma in coaxial gyrotron cavity
leads to downshift of the operational frequency and to decreasing Ohmic loads of both the outer and inner conduc-
tors of coaxial gyrotron cavity.
PACS: 52.35.Hr, 84.40.Ik
INTRODUCTION AND MOTIVATION
Gyrotrons are seen as the most promising configura-
tions for high-power Electron Cyclotron Resonance
Heating (ECRH) and current drive in tokamaks and stel-
larators [1, 2]. New generation of millimeter-wave gyro-
trons developed for plasma heating utilize coaxial cavi-
ties operating in high-order modes. The choice of modes
is dictated by the mode selection requirements and the
admissible level of the heat load on the cavity walls.
These devices can deliver microwave power more than
2 MW and have potentials for further increasing power-
handling capabilities. For example, 170 GHz coaxial
cavity gyrotrons with 2 MW output power are regarded
as potential ECRH sources in ITER [3, 4]. Low density
background plasma appears in the coaxial gyrotron cav-
ity in the long pulse regimes and can influence gyrotron
operation.
The main goal of the work is to study the effect of
low-density background plasma on electromagnetic
properties of the ITER relevant coaxial gyrotron cavity.
For illustration of the results we use parameters of
the 170 GHz, 2 MW, CW coaxial-cavity gyrotron (rele-
vant to the ITER requirements), which is developed in
Karlsruhe Institute of Technology (KIT), For-
schungszentrum Karlsruhe, Germany.
1. MODEL OF A COAXIAL GYROTRON
CAVITY FILLED WITH PLASMA
Due to significant difficulties of the direct analysis
of the plasma-filled coaxial gyrotron cavity we assume
several idealizations. First, instead of the cavity we con-
sider infinitely long coaxial waveguide with perfect
conducting walls. Second, we assume that the inner rod
is smooth (in reality it is corrugated). Also it is assumed
that the waveguide is filled by a homogeneous cold
magnetized plasma with the tensor of dielectric permit-
tivity (1).
We have started our study, considering plasma effect
on cutoff frequencies of the cavity (kz = 0).
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
−=
3
12
21
00
0
0
ε
εε
εε
ε i
i
, (1)
where ( )22
1 11 τξε −−= , ( )22
2 1 ττξε −−= and
2
3 1 ξε −= , ωωξ p= , ωωτ H= , 0
2 εω eep men= ,
eH meB0=ω .
Using Maxwell equations and the dielectric tensor of
plasma (1) we derived the equation for zH in the form
( ) 02 =+Δ ⊥⊥ zHk , (2)
0
1 2
1 2
0,
0,
i
z
z
r R
z
z
r R
H m H
r r
H m H
r r
ε ε
ε ε
=
=
∂⎡ ⎤+ =⎢ ⎥∂⎣ ⎦
∂⎡ ⎤+ =⎢ ⎥∂⎣ ⎦
(3)
where 1
2
2
2
1 εεε −=⊥ kk and 00μεω=k . Boundary
conditions express that tangent electric field at the outer
and inner conductors should be equal to zero.
The solution of (2) with boundary conditions (3) is
where
2 2
1 1
m m m m
mC mCJ J N N
C C C C
ε εχ χ χ χα
ε χ ε χ
⎡ ⎤ ⎡ ⎤⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞′= − + +⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎢ ⎥ ⎢ ⎥
⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎣ ⎦ ⎣ ⎦
oRk⊥=χ and iRRC /0= . The other components of
electromagnetic fields are expressed using zH .
The dispersion relation for determination the cutoff
frequencies for TEm,n mode is
( ) 0)()( 12 =+′ χχεεχ mm ZmZ . (5)
It should be noted that in the case considered cut-off
frequencies of co-rotating (m>0) and counter-rotating
(m<0) modes are different. Assuming 1ε = and 2 0ε =
we come to the dispersion relation for a vacuum coaxial
waveguide.
2. NUMERICAL RESULTS
The dependence of the normalized cutoff frequency
versus the plasma density for the operational mode is
presented in Fig. 1. Calculational parameters are pre-
sented in the Table. As it can be seen, background
plasma leads to decrease of the cutoff frequency.
( ) ( ( ) ( )) ( ),z m m mH r A J k r Y k r AZ k rα⊥ ⊥ ⊥= + ≡ (4)
32 ISSN 1562-6016. ВАНТ. 2012. №6(82)
The effect of plasma on eigenvalues of competing
modes (two triplets {TE35,19; TE34,19; TE33,19} and
{TE-33,20; TE-32,20; TE-31,20}) is demonstrated in Fig. 2.
Parameters of the Coaxcial Gyrotron Cavity
Parameters value
Frequency, GHz 170=f
Magnetic field, T 72.6=B
Operational mode
19,34TE
Inner radius (middle cross-section), cm 8.0=iR
Outer radius(middle cross-section) , cm 955.2=oR
Fig. 1. Dependence of the cut-off frequency for
operational modeon plasma density
Fig. 2 shows that for ‘plasma’ case the pair of modes
(TE-33,20; TE35,19) become closer, as well as (TE-32,20;
TE34,19) and (TE-31,20; TE33,19). Besides, co-rotating and
counter-rotating modes show different behavior versus
plasma density. For co-rotating modes the positive slope
becomes larger and for counter-rotating smaller.
Fig. 2. The effect of plasma on eigenvalues of the most
dangerous competing modes
The effect of plasma density on eigenvalues of
TE34,19 and TE-34,19 modes is demonstrated in the Fig. 3
for fixed value of C, which corresponds to the middle
cross-section of the coaxial gyrotron cavity. One can see
that for co-rotating mode (m > 0) the eigenvalue shift is
negative, and for counter-rotating mode (m<0) the ei-
genvalue shift is positive. In contrast, in the vacuum
case eigenvalues for these modes coincide.
Fig. 3. The effect of plasma density on eigenvalues of
TE34,19 and TE-34,19 modes
In conclusion, we present the plasma influence on
energy characteristics of the coaxial gyrotron cavity. For
this purpose, analytical expression for the energy den-
sity was derived
( ) ( ) ( )
2
2 210
1 2 1 1 2 2 324 2
k
W I I I
k
ω
ωεπμ
ε ε ε ε
⊥
⎧ ⎫′⎪ ⎪⎡ ⎤= + + − +⎨ ⎬⎣ ⎦⎪ ⎪⎩ ⎭
, (6)
where ( )rdrrkZI
R
R
m
i
⊥−∫=
0
2
11 , ( )rdrrkZI
R
R
m
i
⊥+∫=
0
2
12 ,
( )rdrrkZI
R
R
m
i
⊥∫=
0
2
3 .
Using expression (6) the dependence of the linear en-
ergy density (energy per unit length of coaxial gyrotron
cavity) on the plasma density was calculated for fixed
value of radiuses ratio, which corresponds to the middle
cross-section of the coaxial gyrotron cavity (Fig. 4).
One can see that energy increases with increasing
plasma density. The values on Fig. 4 are normalized
with the vacuum value of the linear energy density for
which the axial magnetic field on the outer conductor is
the same.
Fig. 4. The energy content versus plasma density
In order to estimate the effect of the background
plasma on Ohmic losses in the inner conductor we cal-
culated the axial magnetic field on the inner conductor
and compared it with the vacuum value at the same lin-
ear energy density. The results are presented in Fig. 5.
Calculations were made for the middle cross-section of
the coaxial gyrotron cavity.
ISSN 1562-6016. ВАНТ. 2012. №6(82) 33
Fig. 5. The dependence of axial magnetic field on the inner
rod on plasma density
Since the density of Ohmic losses is proportional to
2
zH one can conclude that the background plasma
lead to decreasing of Ohmic losses in the inner rod of
the coaxial gyrotron cavity.
SUMMARY
The analytical model of the plasma-filled coaxial gy-
rotron cavity is developed. The effect of the low-density
plasma on the cutoff frequencies and the RF energy
density of the coaxial gyrotron cavity are studied. It is
assumed that the inner rod is smooth and the coaxial
gyrotron cavity is filled uniformly by a cold low-density
magnetized plasma.
The dispersion relation (5) for cutoff frequencies
(kz=0) is derived taking into account the effect the back-
ground plasma. It is shown that plasma leads to down-
shift of cutoff frequency of the operational mode and
consequently to the downshift the operational frequency
of TE34,19 coaxial cavity gyrotron. The effect of plasma
on frequencies of the triplets of competing modes
{TE35,19; TE34,19; TE33,19} and {TE-33,20; TE-32,20; TE-31,20}
is shown as well (see Fig. 2).
The analytical expression for the RF energy linear
density was derived. Using this expression the depend-
ence of the linear energy density on the background
plasma density was calculated. Also influence of plasma
on Ohmic losses in the outer and inner conductors of
coaxial gyrotron cavity is investigated. It is showed that
plasma lead to increasing the energy density in the co-
axial gyrotron cavity (due to the additional energy of
plasma electrons oscillating in RF field) and decreasing
Ohmic losses in both outer and inner conductor of coax-
ial gyrotron cavity (due to plasma influence on trans-
verse distribution of field in the coaxial gyrotron cav-
ity).
REFERENCES
1. G. Dammertz, S. Alberti, et al. Development of mul-
timegawatt gyrotrons for fusion plasma heating and
current drive // IEEE Trans. Plasma Sci. 2005, v. 52,
№5, p. 808-817.
2. K. McCormick, P. Grigull, et al. New advanced op-
erational regime on the W7-AS stellarator // Phys. Rev.
Lett. 2002, v. 89, №1, p. 015001.
3. J.-P. Hogge, F. Albajar, et al. The European 2 MW,
170 GHz Coaxial Cavity Gyrotron for ITER // The Joint
32nd International Conference on Infrared and Millime-
tre Waves and 15th International Conference on Tera-
hertz Electronics, Cardiff, UK, 2-7 September 2007,
p. 38-40.
4. B. Piosczyk, G. Dammertz, et al. A 2-MW, 170 GHz
Coaxial Cavity Gyrotron // IEEE Transactions on
Plasma Science. 2004, v. 32, №3, p. 413-417.
5. B. Piosczyk, G. Dammertz, et al. Development of
multi-megawatt gyrotrons at Forschungszentrum
Karlsruhe // Twenty-First IEEE/NPS Symposium on
Fusion Engineering, Knoxville, Tennessee, USA,
26-29 September 2005, p. 1-9.
Article received 03.10.12
ВЛИЯНИЕ ФОНОВОЙ ПЛАЗМЫ НИЗКОЙ ПЛОТНОСТИ НА ЧАСТОТНЫЕ
И ЭНЕРГЕТИЧЕСКИЕ ХАРАКТЕРИСТИКИ КОАКСИАЛЬНОГО ГИРОТРОНА
Ю.К. Москвитина, Г.И. Загинайлов, В.И. Ткаченко
Изучено влияние фоновой плазмы низкой плотности на плотность энергии электромагнитного поля в ко-
аксиальном резонаторе гиротрона ITER. Используется модель бесстолкновительной, магнитоактивной
плазмы. Дисперсионное соотношение и выражение для плотности СВЧ-энергии в плазмонаполненном коак-
сиальном резонаторе гиротрона получены аналитически и исследованы численно. Показано, что наличие
плазмы низкой плотности в коаксиальном резонаторе гиротрона приводит к уменьшению рабочей частоты и
уменьшению омических потерь на внешней стенке и внутреннем проводнике резонатора коаксиального ги-
ротрона.
ВЛИВ ФОНОВОЇ ПЛАЗМИ НИЗЬКОЇ ГУСТИНИ НА ЧАСТОТНІ ТА ЕНЕРГЕТИЧНІ
ХАРАКТЕРИСТИКИ КОАКСІАЛЬНОГО ГІРОТРОНА
Ю.К. Москвітіна, Г.І. Загінайлов, В.І. Ткаченко
Вивчено вплив фонової плазми низької щільності на густину енергії електромагнітного поля в коаксіаль-
ному резонаторі гіротрона ITER. Використовується модель беззіткненної, магнітоактивної плазми. Диспер-
сійні співвідношення та вираз для густини НВЧ-енергії в плазмонаповненому коаксіальному резонаторі гі-
ротрона отримані аналітично та досліджені чисельно. Показано, що наявність плазми малої густини в коак-
сіальному резонаторі гіротрона призводить до зменшення робочої частоти та зменшення омічних втрат на
зовнішній стінці та на внутрішньому провіднику резонатора коаксіального гіротрона.
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