Neoclassical transport in KOLER trap (Yamator)
The new stellarator type magnetic system having a high magnetic well value was proposed in paper [1]. In the present work neoclassical transport for magnetic configuration of l = 2 variant of similar system is investigated by numerical methods. A so-called 1/ ν transport regime, in which the transpo...
Gespeichert in:
| Datum: | 2000 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2000
|
| Schriftenreihe: | Вопросы атомной науки и техники |
| Schlagworte: | |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/78484 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Neoclassical transport in KOLER trap (Yamator) / V.N. Kalyuzhnyj, S.V. Kasilov, V.V. Nemov // Вопросы атомной науки и техники. — 2000. — № 6. — С. 29-31. — Бібліогр.: 5 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-78484 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-784842015-03-19T03:02:02Z Neoclassical transport in KOLER trap (Yamator) Kalyuzhnyj, V.N. Kasilov, S.V. Nemov, V.V. Magnetic confinement The new stellarator type magnetic system having a high magnetic well value was proposed in paper [1]. In the present work neoclassical transport for magnetic configuration of l = 2 variant of similar system is investigated by numerical methods. A so-called 1/ ν transport regime, in which the transport coefficients are increased with reduction of particle collision frequency ν is considered. For calculating of transport coefficients a technique [2], based on integration along magnetic field lines in given stellarator magnetic field with taking into account particles trapped not only within one magnetic field period but also within several magnetic field periods is used. The obtained transport coefficients are presented in a standard form containing a factor depending on the magnetic field geometry. The dependence of transport coefficients from value of a resulting vertical magnetic field is analysed. 2000 Article Neoclassical transport in KOLER trap (Yamator) / V.N. Kalyuzhnyj, S.V. Kasilov, V.V. Nemov // Вопросы атомной науки и техники. — 2000. — № 6. — С. 29-31. — Бібліогр.: 5 назв. — англ. 1562-6016 http://dspace.nbuv.gov.ua/handle/123456789/78484 533.9 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Magnetic confinement Magnetic confinement |
| spellingShingle |
Magnetic confinement Magnetic confinement Kalyuzhnyj, V.N. Kasilov, S.V. Nemov, V.V. Neoclassical transport in KOLER trap (Yamator) Вопросы атомной науки и техники |
| description |
The new stellarator type magnetic system having a high magnetic well value was proposed in paper [1]. In the present work neoclassical transport for magnetic configuration of l = 2 variant of similar system is investigated by numerical methods. A so-called 1/ ν transport regime, in which the transport coefficients are increased with reduction of particle collision frequency ν is considered. For calculating of transport coefficients a technique [2], based on integration along magnetic field lines in given stellarator magnetic field with taking into account particles trapped not only within one magnetic field period but also within several magnetic field periods is used. The obtained transport coefficients are presented in a standard form containing a factor depending on the magnetic field geometry. The dependence of transport coefficients from value of a resulting vertical magnetic field is analysed. |
| format |
Article |
| author |
Kalyuzhnyj, V.N. Kasilov, S.V. Nemov, V.V. |
| author_facet |
Kalyuzhnyj, V.N. Kasilov, S.V. Nemov, V.V. |
| author_sort |
Kalyuzhnyj, V.N. |
| title |
Neoclassical transport in KOLER trap (Yamator) |
| title_short |
Neoclassical transport in KOLER trap (Yamator) |
| title_full |
Neoclassical transport in KOLER trap (Yamator) |
| title_fullStr |
Neoclassical transport in KOLER trap (Yamator) |
| title_full_unstemmed |
Neoclassical transport in KOLER trap (Yamator) |
| title_sort |
neoclassical transport in koler trap (yamator) |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2000 |
| topic_facet |
Magnetic confinement |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/78484 |
| citation_txt |
Neoclassical transport in KOLER trap (Yamator) / V.N. Kalyuzhnyj, S.V. Kasilov, V.V. Nemov // Вопросы атомной науки и техники. — 2000. — № 6. — С. 29-31. — Бібліогр.: 5 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT kalyuzhnyjvn neoclassicaltransportinkolertrapyamator AT kasilovsv neoclassicaltransportinkolertrapyamator AT nemovvv neoclassicaltransportinkolertrapyamator |
| first_indexed |
2025-07-06T02:34:04Z |
| last_indexed |
2025-07-06T02:34:04Z |
| _version_ |
1836863187604996096 |
| fulltext |
UDC 533.9
NEOCLASSICAL TRANSPORT IN KOLER TRAP (YAMATOR)
V.N.Kalyuzhnyj, S.V.Kasilov, V.V.Nemov
Institute of Plasma Physics,
National Science Centre “ Kharkiv Institute of Physics and Technology”,
Akademichna 1, Kharkiv 61108, Ukraine.
The new stellarator type magnetic system having a high magnetic well value was proposed in paper [1]. In the
present work neoclassical transport for magnetic configuration of l = 2 variant of similar system is investigated by
numerical methods. A so-called 1 / ν transport regime, in which the transport coefficients are increased with
reduction of particle collision frequency ν is considered. For calculating of transport coefficients a technique [2],
based on integration along magnetic field lines in given stellarator magnetic field with taking into account particles
trapped not only within one magnetic field period but also within several magnetic field periods is used. The
obtained transport coefficients are presented in a standard form containing a factor depending on the magnetic field
geometry. The dependence of transport coefficients from value of a resulting vertical magnetic field is analysed.
1. Introduction
In Ref. [1] a new stellarator system has been
proposed which is characterized by an increased
magnetic well value. The magnetic field of such a
system is produced by pairs of helical conductors with
oppositely directed currents of the same value. The
conductors wind with equal pitch values on the nested
tori with the same major radii R0 and different small
radii r1 and r r r2 1= + ∆ . High magnetic well values
in the proposed stellarator systems suggest a possibility
of an MHD stability of plasma in such systems. At the
same time the question about transport properties of
such a system stays open.
As it is known, one of possible reasons for the
increased heat and energy losses in stellarator type
systems (together with so-called “anomalous” losses) is
the neoclassical transport due to the asymmetry of
stellarator magnetic field. According to the theory,
different transport regimes are possible in asymmetric
system however the most dangerous regime is the so-
called 1 / ν -regime where transport coefficients increase
with decreasing collision frequency ν . Therefore, the
reduction of transport coefficients in 1 / ν regime is one
of important requirements in the optimization of
stellarator systems [3]. This transport regime is studied
in the present paper for l = 2 configuration of the
system proposed in Ref. [1].
2. Method and results of numerical
investigation
The method of Ref. [2] is used in the present paper
for evaluation of transport coefficients. Based on the
field line integration technique, this method takes into
account particles trapped within one or several magnetic
field periods. In accordance with this method transport
in 1 / ν regime can be described by a standard
expression for the magnetic surface averaged particle
flux density (or similar formula for the energy flux
density),
n
L
effF R
dze z
A z
n
f
f
r
T z
= −
−∞
∫
8
9 3 2
2
2
3 2
5 2
0
0
0
2
/
/
/
( )π
ρ
ν ε
∂
∂
v
where f 0 is the Maxwellian distribution function which
is a function of particle energy and magnetic surfaces,
A z( ) is a quantity connected with collision operator,
vT and ρL are the thermal velocity and the
characteristic particle Larmor radius, R is the major
torus radius, ∂ ∂f r0 is the averaged derivative of f 0
over the normal to the magnetic surface, εeff is the
effective amplitude of modulation ( non-uniformity ) of
the magnetic field along the magnetic field line
(“effective ripple”). The given formula differs from the
corresponding formula for the standard stellarator (see
eq. (2.16) of Ref. [4]) by the replacement of the helical
modulation amplitude εh with the quantity εeff . (“The
standard stellarator” means here a stellarator magnetic
field with the circular magnetic axis and magnetic
surfaces with circular cross-section.) The value of εeff
is obtained by means of numerical integration over the
magnetic field line length for the given magnetic field
and over the perpendicular adiabatic invariant (see Ref.
[2]). εeff coincides with εh for the standard stellarator.
Thus, the parameter εeff contains all the information
about the effect of the magnetic field geometry in the
considered transport regime. The transport coefficients
in 1 / ν regime for any magnetic configuration can be
obtained from the corresponding transport coefficients
of the standard stellarator by replacement of εh
3 2 with
εeff
3 2 . Note that the energy flux density differs from the
given formula for the particle flux density by the factor
zT in the sub-integrand.
60 80 100 120 140
-40
-20
0
20
40
60 80 100 120 140
-40
-20
0
20
40
Fig.1. Magnetic surface cross-section for B⊥ = 0
0.00 0.10 0.20 0.30
0.0
0.1
0.2
0.3
0.4 ι
r/R
KLR (o)
KLR (i)
Fig.3. The rotational transform angle ι versus the
average magnetic surface radius r R0
60 80 100 120 140
-40
-20
0
20
40
60 80 100 120 140
-40
-20
0
20
40
Fig.2. Magnetic surface cross-section for B⊥ ≠ 0
0.00 0.10 0.20 0.30
1E-4
1E-3
1E-2
1E-1
1E+0 ε3/2
eff
r/R
KLR (o)
KLR (i)
U-3M (i)
U-3M (o)
Fig.4. Results of εeff
3 2 calculation for l = 2 KOLER
trap (KLR) and for Uragan-3M torsatron (U-3M)
The l = 2 variant of the proposed system chosen for
the numerical evaluation has the following parameters,
r R1 0 0 3= . , r R2 0 0 45= . , ∆r R0 015= . . The
evaluation was performed assuming thin conductors
placed at the toroidal surfaces along the helical line
θ ϕ= n where θ and ϕ are poloidal and toroidal
angles and n is a number of poloidal turns of the helical
line after one toroidal turn ( n = 3 ). The initial
magnetic field of the system consisted from the field of
helical conductors and toridal magnetic field
B B Rϕ ρ= 0 0 ( ρ is the distance from the main axis
of torus). The magnetic field of helical conductors has
been calculated with the help of Biot-Savart law. In
order to study the possibility to change transport
coefficients the calculation was performed both for the
initial configuration and the analogous configuration
with the additional uniform vertical magnetic field. The
value of vertical field corresponded to the return of the
magnetic axis to the circular axis of torus. The magnetic
surface cross-sections for these two cases are shown in
Figs. 1 and 2. The corresponding radial dependencies of
the rotational transform angle are shown in Fig. 3. The
results of the calculation of εeff
3 2 for these two
configurations are given in Fig. 4. For the comparison,
the values of εeff
3 2 for the torsatron Uragan-3M are
shown at the same plot for two opposite values of the
total vertical magnetic field. These values correspond to
the shift of the magnetic configuration to the inner or
outer side of the torus. The absolute value of the vertical
field B⊥ was of the order of 1.2% of the toroidal field of
the torsatron.
3.Conclusion
It follows from the obtained results that the initial
configuration is characterized by increased values of
transport coefficients, which exceed approximately by
one order of magnitude the corresponding coefficients
for U-3M with the shift of magnetic surfaces to the outer
side of torus. On the other hand, the later coefficients
exceed the corresponding coefficients for the standard
stellarator 2-6 times. As it follows from the calculation,
the values of transport coefficients can be reduced by
order of magnitude or even more with addition of the
vertical field that shifts the magnetic configuration to the
inner side of torus. For rather large r R0 values these
coefficients exceed corresponding coefficients for U-3M
(shift of the magnetic configuration to the inner side of
torus), while for the values of r R0 within the limits
reached in U-3M they can even be smaller than for U-
3M. We should note that such vertical field may cause
the decrease of the magnetic well.
Also, we have considered the neoclassical transport
in 1 / ν regime for l = 3 variant of the proposed system
[5]. In this case the results for the parameter εeff
3 2
appeared to be similar to the results for l = 2 system.
References
1. V.G.Kotenko, G.G.Lesnyakov, S.S.Romanov.
Stellarator Fields with 2-wire Lines Wound Round the
Torus // Voprosy Atomnoj Nauki I Tekhniki (Problems
of Atomic Science and Technology, Series “Plasma
physics”), 1999, issuses 1(1), 2(2), pp.49-51.
2. V.V.Nemov, S.V.Kasilov, W.Kernbichler, M.F.Heyn.
Evaluation of 1/ν neoclassical transport in stellarators //
Phys. Plasmas, 1999, vol.6, №12, pp.4622-4632.
3. G.Grieger, W.Lotz, P.Merkel at al. Physics
optimization of stellarators // Phys. Fluids B, 1992,
vol.4, №7, pp.2081-2091.
4. Galeev A.A., Sagdeev R.Z. “Neoklassicheskaja”
teorija diffuzii //Voprosy Teorii Plasmy (Reviews of
Plasma Physics), Ed. M.A.Leontovich, Moscow:
Energoatomizdat, 1973, vol.7, pp.205-273 (in Russian).
5. V.G.Kotenko, G.G.Lesnyakov, S.S.Romanov.
Yamator: high magnetic-well value stellarators // J.
Plasma Fusion Res. SERIES, 2000, vol.3, PI-8.
UDC 533.9
References
|