Angles of rotational transform behavior with plasma pressure variations in the torsatron
Збережено в:
| Опубліковано в: : | Вопросы атомной науки и техники |
|---|---|
| Дата: | 2002 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2002
|
| Теми: | |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/77821 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Angles of rotational transform behavior with plasma pressure variations in the torsatron / Yu.K. Kuznetsov, I.B. Pinos, V.I. Tyupa // Вопросы атомной науки и техники. — 2002. — № 5. — С. 15-17. — Бібліогр.: 10 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859796958502191104 |
|---|---|
| author | Kuznetsov, Yu.K. Pinos, I.B. Tyupa, V.I. |
| author_facet | Kuznetsov, Yu.K. Pinos, I.B. Tyupa, V.I. |
| citation_txt | Angles of rotational transform behavior with plasma pressure variations in the torsatron / Yu.K. Kuznetsov, I.B. Pinos, V.I. Tyupa // Вопросы атомной науки и техники. — 2002. — № 5. — С. 15-17. — Бібліогр.: 10 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| first_indexed | 2025-12-02T14:09:36Z |
| format | Article |
| fulltext |
ANGLES OF ROTATIONAL TRANSFORM BEHAVIOR WITH PLASMA
PRESSURE VARIATIONS IN THE TORSATRON
Yu.K. Kuznetsov, I.B. Pinos, V.I. Tyupa
National Science Center “Kharkiv Institute of Physics and Technology”, Akademichna st.1,
Kharkiv, 61108, Ukraine
PACS: 52.55.Hc
1. INTRODUCTION
At present, rather high plasma pressure values
are obtained with stellarator systems. Yet, as is known,
the plasma pressure can affect both the angle of rotational
transform and the mean magnetic well value [1-7]. With
an increasing plasma pressure the magnetic axis is
displaced to the outward of the torus, and this can lead to
an increase in the angle of rotational transform on the
magnetic axis, a decrease in the magnetic system shear,
and also, to stripping of outer magnetic surfaces (i.e.,
decrease in the plasma radius). The presence of various
resonance perturbations at a small shear of field lines can
cause the magnetic surfaces to split into separate rosettes.
The existence of rosettes, great in size, essentially reduces
the stability of magnetic surfaces in closed helical traps
[8, 9]. On the other hand, an increasing displacement,
rc/r0, gives rise to the magnetic well, and this results in the
removal of restriction on the ultimate plasma-stability
pressure for some most dangerous MHD instabilities. In
view of this, it is of importance to know the distributions
of both the angle of rotational, determined by plasma
pressure.
For different plasma pressure profiles, the
authors have calculated the angles of rotational transform
as functions of the parameter α that characterizes the
profile of vacuum angles of field line rotation. Three laws
of plasma pressure distribution over vacuum magnetic
surfaces were considered: P=P0, P=P0(1-ψ(r)/ψ(r0));
P=P0(1-ψ(r)/ψ(r0))2, where P0 is the plasma pressure on
the magnetic axis, ψ(r) is the averaged function of
vacuum magnetic surfaces. The distribution of vacuum
angle of rotational transform was calculated as t(r)=t(r0)[α
+(1-α)r2/r2
0], where α=t(0)/t(r0) is the ratio of the angle of
field line rotation on the magnetic axis to its value at the
plasma boundary of radius r0.
2. ANALYTICAL CALCULATIONS
The angles of rotational transform due to
different plasma pressure profiles were calculated by the
analytical formulae derived with the use of the formulae
for averaging over magnetic surfaces [5, 6, 10]. For the
distributions P=P0 and P=P0(1-ψ(r)/ψ(r0)) the angle of
rotational transform was calculated by the following
expression
)1(,))1/(11(
)1(4
1
)1(
)(
)(
22
2
22
0
1
cb
b
cc
bca
rt
rt
+−−
+
−
−+=
><
where a, b, c are written for the P = P0 pressure
distribution as
2
2
2
1
2
2
2
2
1
1,)1(3
,)1(2)1(
o
c
o
c
o
c
o
r
r
a
c
r
rr
a
b
r
r
r
r
a
α−=α−=
α−+α−+α=
(2)
For the distribution P=P0(1-ψ(r)/ψ(r0)), these coefficients
have the following form:
.
2/31
2/)1(11
;
2/31
/1)(1(2
2
3
;
2/31
2/)1(1
2)1(
22
22
2
2
22
22
2
1
22
22
2
2
2
2
1
oc
oc
o
c
oc
oc
o
c
oc
oc
o
c
o
rr
rr
r
r
a
c
rr
rr
ar
rr
b
rr
rr
r
r
r
r
a
−
α−−α−=
−
−α−+α
=
−
α−−
+α−+α=
(3)
For the distribution P=P0(1-ψ(r)/ψ(r0))2 the angle of field
line rotation was calculated as
)4(,
)(
2
1)(
2
1
)(
)(
111
1
1
q
DC
qpq
BA
qp
aa
rt
rt
o
+
+
++
+
=
=
><
(4)
where
D
q
p
q
q q
p p
p
q
q q
p p
q
q
p q
p
q
=
+ +
−
−
− − −
−
−
− − +
1
1
1
1
1
1
1
1
1 1
1
1
3
1
3
1
( )
( )
,
,
)1(13
,1,
13)1(
1
11
1
11
11
pp
q
qD
q
p
C
q
qDB
pp
q
p
q
qD
A
−
−−−−
=
−=
−
++−−
=
where
,,
6
,
48
,
2
48
,
48
,
2
48
32133
1
2
1
11
1
1
2
11
1
1
2
1
111
2
11
ooooooo pqE
c
EqEqy
cby
dyb
yq
cbyb
p
cby
dyb
yq
cbyb
p
+=+−−++−=
−+
−
−=
−+−
=
−+
−
+=
−++
=
Problems of Atomic Science and Technology. 2002. № 5. Series: Plasma Physics (8). P. 15-17 15
where
p
bd e c
q
c cbd eb d ec
a b c d e
b
b c d e
a
c
c e
a
d
b c d e
a
e
b c d e
a
o
o
=
−
−
= − + −
+
+
= − + − +
=
− − + −
=
− +
=
+ − − −
=
+ + + +
1 1 1 1
2
1
3
1 1 1 1 1
2
1
2
1 1
1
1
1
1
1
1
1
1
1
4
12 36
216 48 16 6
1
4 2 4 14 28
6 10 70
4 2 4 14 28
1
,
,
,
,
,
)6(,
)1(3
2,
)1)((
])1(
4
75[3
1
2
3
2
/]/)1([
)5(,)1(
],)1(
4
5)1(
4
5[
3
]},/)1(2/9/])1(42[4
/)1(2/9/82[
/)1{(/
]},/)1(4/7
/]/)1(2/9[5
)/)1(2/15
/91(3[/)1(3{/
},/)1(3/]/)1(32[3
/)1(3/62{/2
/)1(2/)1(
2
6
6
4
4
2
2
22
5
2
1
3
2
2
1
2
2
3
1
2
44
1
22
1
22
4422
44
1
22
1
22
44
22
1
44
1
22
1
22
4422
2222
1
α+
=
α+
β
=
α−+α+−
α+
α+
α−+α
=
α−−=
α−+α−+α−=
α−+α−+α
+α−+α+−−
−α−=
α−+
α−+α+
+α−+
+α+−−α−=
α−+α−+α+
+α−+α+−−
−α−+α−+α=
M
rt
A
r
r
r
r
M
r
r
rrrr
N
r
rr
a
MNe
r
r
r
r
ar
rMNr
d
rMrrrrrM
rrMrMrN
rrarrc
rMr
rrrrM
rrM
rrMNrrarrb
rrMrrrrM
rrMrrMrNr
rrrra
o
o
o
c
o
c
o
c
ococ
o
c
oo
c
o
c
oooc
ococ
ococ
o
ooc
oc
ococo
oooc
ocococ
oco
where A0 = R/r0 is the aspect ratio, R is the major radius
of the torus, β = P0/(H2/8π) is the plasma pressure-to-
magnetic pressure ratio.
Figures 1,2 show the angles of rotational
transform determined by different plasma pressure
profiles as functions of the average radius r1/r0 for the
magnetic axis displacement rc/r0 = 0.3. The plots are given
for the parameter α that characterizes the profile of the
vacuum angle of rotational transform (Fig.1: a- α=0, b- α
=0.2, c- α=0.4; Fig.2: a- α=0.6, b- α=0.8, c- α=1.0).
3. CONCLUSIONS
The calculations have shown that for the magnetic
systems with a great magnetic shear (α<<1, Uragan-3M)
the distributions of angles of field line rotation (Fig.1 a, b)
are weakly dependent on the plasma pressure profiles (at
the same magnetic axis displacements rc/r0).
Fig.1. Distributions of angles of rotational transforms resulting
from different plasma pressure profiles R/r0 =8.9 (1: P=P0; 2:
P=P0(1-ψ(r)/ ψ(r0)); 3: P=P0(1-ψ(r)/ ψ(r0))2; 4: P=0)
16
a
b
c
(5)
(6)
As α increases (shear of vacuum-configuration field lines
decreases), the behavior of angles of field line rotation
specified by different plasma pressure profiles becomes
different (Fig.2 a, c)/ The sharper distribution P=P0(1-
ψ(r)/ ψ(r0))2 gives rise to large angles of rotational
transform in the central region of the magnetic
configuration. This reduces the shear and, in the presence
of resonance perturbations, can cause the magnetic
surfaces to split.
With α approaching unity (small shear of field lines) and
at P=P (sloping distribution), the vacuum angle of
rotational transform practically retains its initial profile
(Fig.2 b, c). This means that the magnetic surfaces are
displaced under the plasma pressure to the outward of the
torus without changing their form.
REFERENCES
1. Kovrizhnykh L.M., Shchepetov S.V. Fiz. Plasmy,
1981, v.7, is 2., pp. 419-427.
2. Pyatov V.N., Sebko V.P., Tyupa V.I. Preprint KFTI
76-25 (in Russian) Kharkov, 1976.
3. Kuznetsov Yu.K., Pinos I.B., Tyupa V.I. VANT,
Problems of Atomic Science and Technology, Series:
Plasma physics, vol.6(6), (2000), p. 52-54.
4. Kuznetsov Yu.K., Pinos I.B., Tyupa V.I. 23 rd EPS
Conf. on Controlled Fusion and Plasma Physics,
Kiev, Ukraine (1996) 20C, part II, p. 535.
5. Kuznetsov Yu.K., Pinos I.B., Tyupa V.I. IAEA
Techn. Comm. Meeting 8 th Stellarator Workshop,
Kharkov, USSR, 1991, IAEA, Vienna 317 (1991).
6. Kuznetsov Yu.K., Pinos I.B., Tyupa V.I.VANT,
Problems of Atomic Science and Technology, Series:
Plasma physics, vol. 1(1), 2(2), (1999), p. 52-54.
7. Pustovitov V.D. Fiz. Plasmy, v.14, p.522, 1988.
8. Danilkin I.S. Stellarators, Nauka Press, Moscow, v.
65, p.50, 1973.
9. Aleksin V.F., Pyatov V.N., Sebko V.P. Tyupa V.I.
Fiz. Plasmy, v.2, p. 219, 1976.
10. Solovyov L.S., Shafranov V.D. Vopr. Teor. Plasmy,
Gosatomizdat, Moscow, v. 5, p. 3, 1967. (in
Russian).
Fig.2. Distributions of angles of rotational transforms
resulting from different plasma pressure profiles R/r0
=8.9 (1: P=P0; 2: P=P0(1-ψ(r)/ ψ(r0)); 3: P=P0(1-ψ(r)/
ψ(r0))2; 4: P=0)
17
c
b
a
18
|
| id | nasplib_isofts_kiev_ua-123456789-77821 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-02T14:09:36Z |
| publishDate | 2002 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Kuznetsov, Yu.K. Pinos, I.B. Tyupa, V.I. 2015-03-07T15:38:31Z 2015-03-07T15:38:31Z 2002 Angles of rotational transform behavior with plasma pressure variations in the torsatron / Yu.K. Kuznetsov, I.B. Pinos, V.I. Tyupa // Вопросы атомной науки и техники. — 2002. — № 5. — С. 15-17. — Бібліогр.: 10 назв. — англ. 1562-6016 PACS: 52.55.Hc https://nasplib.isofts.kiev.ua/handle/123456789/77821 en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Magnetic confinement Angles of rotational transform behavior with plasma pressure variations in the torsatron Article published earlier |
| spellingShingle | Angles of rotational transform behavior with plasma pressure variations in the torsatron Kuznetsov, Yu.K. Pinos, I.B. Tyupa, V.I. Magnetic confinement |
| title | Angles of rotational transform behavior with plasma pressure variations in the torsatron |
| title_full | Angles of rotational transform behavior with plasma pressure variations in the torsatron |
| title_fullStr | Angles of rotational transform behavior with plasma pressure variations in the torsatron |
| title_full_unstemmed | Angles of rotational transform behavior with plasma pressure variations in the torsatron |
| title_short | Angles of rotational transform behavior with plasma pressure variations in the torsatron |
| title_sort | angles of rotational transform behavior with plasma pressure variations in the torsatron |
| topic | Magnetic confinement |
| topic_facet | Magnetic confinement |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/77821 |
| work_keys_str_mv | AT kuznetsovyuk anglesofrotationaltransformbehaviorwithplasmapressurevariationsinthetorsatron AT pinosib anglesofrotationaltransformbehaviorwithplasmapressurevariationsinthetorsatron AT tyupavi anglesofrotationaltransformbehaviorwithplasmapressurevariationsinthetorsatron |