Effect of the lower hybrid heating on the confinement of high energy ions in stellarators
In a stellarator-type device, the effect of the lower hybrid (LH) heating on the ion confinement is investigated. For this purpose, the motion of high energy ions is simulated numerically in the Large Helical Device, as an example of such a device. It is shown that owing to LH heating, initially wel...
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2002
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| Zitieren: | Effect of the lower hybrid heating on the confinement of high energy ions in stellarators / D.L. Grekov, M.S. Smirnova // Вопросы атомной науки и техники. — 2002. — № 5. — С. 21-23. — Бібліогр.: 14 назв. — англ. |
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irk-123456789-778822015-03-09T03:02:00Z Effect of the lower hybrid heating on the confinement of high energy ions in stellarators Grekov, D.L. Smirnova, M.S. Magnetic confinement In a stellarator-type device, the effect of the lower hybrid (LH) heating on the ion confinement is investigated. For this purpose, the motion of high energy ions is simulated numerically in the Large Helical Device, as an example of such a device. It is shown that owing to LH heating, initially well-confined particles are expelled from the plasma in time less then the ion-electron collisional time. Therefore, it is possible to use this method of heating for helium ash removal in a stellarator-reactor. 2002 Article Effect of the lower hybrid heating on the confinement of high energy ions in stellarators / D.L. Grekov, M.S. Smirnova // Вопросы атомной науки и техники. — 2002. — № 5. — С. 21-23. — Бібліогр.: 14 назв. — англ. 1562-6016 PACS: 52.55.Hc http://dspace.nbuv.gov.ua/handle/123456789/77882 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Magnetic confinement Magnetic confinement |
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Magnetic confinement Magnetic confinement Grekov, D.L. Smirnova, M.S. Effect of the lower hybrid heating on the confinement of high energy ions in stellarators Вопросы атомной науки и техники |
| description |
In a stellarator-type device, the effect of the lower hybrid (LH) heating on the ion confinement is investigated. For this purpose, the motion of high energy ions is simulated numerically in the Large Helical Device, as an example of such a device. It is shown that owing to LH heating, initially well-confined particles are expelled from the plasma in time less then the ion-electron collisional time. Therefore, it is possible to use this method of heating for helium ash removal in a stellarator-reactor. |
| format |
Article |
| author |
Grekov, D.L. Smirnova, M.S. |
| author_facet |
Grekov, D.L. Smirnova, M.S. |
| author_sort |
Grekov, D.L. |
| title |
Effect of the lower hybrid heating on the confinement of high energy ions in stellarators |
| title_short |
Effect of the lower hybrid heating on the confinement of high energy ions in stellarators |
| title_full |
Effect of the lower hybrid heating on the confinement of high energy ions in stellarators |
| title_fullStr |
Effect of the lower hybrid heating on the confinement of high energy ions in stellarators |
| title_full_unstemmed |
Effect of the lower hybrid heating on the confinement of high energy ions in stellarators |
| title_sort |
effect of the lower hybrid heating on the confinement of high energy ions in stellarators |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2002 |
| topic_facet |
Magnetic confinement |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/77882 |
| citation_txt |
Effect of the lower hybrid heating on the confinement of high energy ions in stellarators / D.L. Grekov, M.S. Smirnova // Вопросы атомной науки и техники. — 2002. — № 5. — С. 21-23. — Бібліогр.: 14 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT grekovdl effectofthelowerhybridheatingontheconfinementofhighenergyionsinstellarators AT smirnovams effectofthelowerhybridheatingontheconfinementofhighenergyionsinstellarators |
| first_indexed |
2025-07-06T02:07:49Z |
| last_indexed |
2025-07-06T02:07:49Z |
| _version_ |
1836861535683608576 |
| fulltext |
EFFECT OF THE LOWER HYBRID HEATING ON THE CONFINEMENT
OF HIGH ENERGY IONS IN STELLARATORS
D.L.Grekov, M. S. Smirnova
Institute of Plasma Physics,
National Science Center "Kharkov Institute of Physics and Technology",
61108, Kharkov, Ukraine
In a stellarator-type device, the effect of the lower hybrid (LH) heating on the ion confinement is investigated. For this purpose, the
motion of high energy ions is simulated numerically in the Large Helical Device, as an example of such a device. It is shown that owing
to LH heating, initially well-confined particles are expelled from the plasma in time less then the ion-electron collisional time. Therefore,
it is possible to use this method of heating for helium ash removal in a stellarator-reactor.
PACS: 52.55.Hc
As a result of the development of the concept of a drift-optimized
stellarator configuration, the main requirement for a construction
of current devices is single particle confinement in the plasma core
region during a long time. The Large Helical Device [1] (LHD)
with the magnetic axis shifted inwardly with respect to the
geometrical center is an example of such a configuration with an
improved particle confinement [2,3]. As the simulation of a single
particle motion shows, in such a configuration the high energy ion
confinement time (tic) exceeds significantly the ion-electron
collisional time [2,3] e/i
Eτ . Besides, the confinement of high
energy ions in the core region depends weakly on the particle pitch
value λ at the start point (here λ=V|| /V with V|| being the parallel
velocity of the particle motion along the magnetic field lines, and
V the full particle velocity) (see Fig.1). From the tokamak
experiments (see, for example, [4,5] it is well known that at the
lower hybrid (LH) heating of tokamak plasmas, the regime of ion
stochastic heating [6,7] can be realized. In this case the ions with
⊥⊥ ≥ kV ω ( ⊥V is the velocity component of the particle
motion perpendicular to the magnetic field lines, ⊥k is the LH
wave vector in the same direction, and ω is the wave frequency)
get the perpendicular kinetic energy. Keeping in mind the weak
dependence of tic on λ, it is interesting to clarify the following
question: whether the LH heating could affect the high energy ion
confinement in a stellarator. While solving this problem, we
should take into account some important features. The ions
motion is the result of two actions. The first one is the ion guiding
center motion in the confining magnetic field. It is modified by the
LH heating due to the change of both the ion kinetic energy and
pitch. The second one is the ion cyclotron rotation and the ion
interaction with LH wave during this rotation. It is also modified at
the guiding center motion because of a space change in both the
LH wave amplitude and conditions of the wave-particle
interaction.
It is known that the drift approximation is valid for description of
charged particle motion in stellarators, if the magnetic field
variations in space and time are small within the Larmor radius
cL /V ωρ ⊥= and the Larmor period cL /T ωπ2= (
mceBc 0=ω is the cyclotron frequency). The heliotron
configuration, as considered in the paper, is characterized by
comparatively large value of B 0 = 3T and a small value of the
inverse aspect ratio (a p /R=0.16). In such a configuration, drift
approximation can be used even for fast particles with energies W
> 100 keV.
In heliotrons, the representation of the magnitude of the magnetic
field along a field line requires the following expansion in a
Fourier series:
B/B 0 = )r(N,j
j N
∑ ∑
∞
=
∞
− ∞=0
ε cos(jθ - NMφ). (1)
Here r, θ and φ are magnetic coordinates [9], where r is the
radial coordinate normalized by the plasma radius pa and related
to the flux surface label as ψ = B 0 r2/2; θ and φ are the poloidal
and toroidal angle-like variables, respectively; j is the poloidal
mode number, N is the toroidal mode number, M is the number
of magnetic field periods along the device length, B0 is the
averaged value of the magnetic field at the geometrical axis of the
device. Guiding center motion of a charged particle in heliotrons
is described in magnetic coordinates by the following equations
[8]:
,bV
dt
dr
t
D
θε ∂
∂−= ,
r
bV
dt
d
t
D
∂
∂=
ε
θ 0
,bV
dt
dV
Dc
||
φ
ω
∂
∂−= .
dt
d
φ
φ Ω= (2)
Here b = B/B 0 ; θ 0 = θ − ι φ is the field line label, and the
rotational transform ι is related to the poloidal flux 2πψ p and
the toroidal flux 2πψ as ι = − dψ p /dψ. In Eq. (2), V D =V B∇
+V cur is the particle drift velocity due to the gradient−B drift (V
B∇ ) and the curvature drift (V cur ), where V B∇ =µc/(eR), and V
cur = mcV 2
|| /(eBR), µ is the particle magnetic moment;
R/V||=Ω φ is the toroidal transit frequency. The last closed
flux surface was adopted as a loss boundary.
Let us consider the cyclotron motion of the high energy ion with
the perpendicular velocity V⊥ and its interaction with LH wave of
amplitude Е0. Our simulation of the ion stochastic heating in a
heliotron is based on the classical Karney’s papers [6,7]. The ion
stochastic heating takes place when the following conditions are
satisfied:
min
/
B
E
N αννα =>= ⊥ 4
32
0 , (3)
( ) ( ) 3231 42 //
maxLHmin rrr α νπαν =<<−= . (4)
Here ωckN ⊥⊥ = is the perpendicular component of the LH
wave refractive index, ciωων = , ωci is the cyclotron frequency
Problems of Atomic Science and Technology. 2002. № 5. Series: Plasma Physics (8). P. 21-23 21
of high energy ions, ciLH Vkr ω⊥⊥= . We now assume that the
frequency is higher than ω pI (0) (with ω pI (0) being the bulk ions
plasma frequency at the magnetic axes), thus the LH resonance
will not be located in plasma. With a proper choice of the initial
value of N || (N || is the parallel component of refractive index),
the electron Landau damping and bulk ion stochastic heating will
be negligibly small [10]. The high energy ions happen to be the
only kind of particles which interact with the wave. Using the
results of the studies of propagation and absorption of LH waves
in stellarators [10] we will approximate the space variation of N ||
as follows:
)bC(NN 10 1 += | || | . (5)
where N ||0 and С1 are constants. We put
( ))r()r(mm pIpIeI
222
13 ωωωεε −⋅≈ (me and mI are
the
electron and bulk ion mass), | |⊥ ≈ NN 13 εε . Since
| || || |⊥⊥ > >≈ ENENE , then ⊥≈ EE0 . Thus, Е0 varies
when the interacting ion moves along its trajectory.
Because of assuming the density of high energy ions to be low, the
LH wave absorption is small. As a consequence, the LH waves
propagate from antenna to plasma core and back to plasma edge,
and spread over the whole plasma volume. Owing to the
dependence of the wave parameters on both space coordinates
and change in V⊥ at the motion of ion guiding center, the
interaction conditions (3) and (4) will vary from point to point.
Defining the phase of wave-ion interaction as
0ϕωϕ +−= | || | t)Vk( (with 0ϕ being the initial random phase)
we write the difference equation in the form:
−−−+=+
4
21221 πνννϕν
LH
/
LH
i
LH
i
LH
i
LH r
arccos)r(cos)cos(A
r
rr , (6)
−−−
−
−=+
4
2122
2
22
1 πνννϕ
ν
LH
/
LH
i
LH
LHii
r
arccos)r(cos)cos(A
r
r
tt . (7)
where А is directly related to α.
For the beginning let us consider the high energy ion motion in
the LHD magnetic field when the wave-particle interaction is
absent. As an example we calculate the trace of the passing ion
with energy keVW 100= and pitch 60.=λ . The
coordinates of the ion starting position are r = a p /2, θ0 = π/6, φ0
= 0 (Figs. 2, 3). When starting outside the torus and moving
counterclockwise, this passing particle is well confined. When
collisions are neglected, the ion confinement time exceeds
considerably the ion-electron collisional time e/i
Eτ .
Now we will study the motion of ions affected by LH heating. For
plasma and LH wave parameters we put 314100 −= cm)(nI ,
851.)0(/ pI =ωω , 17550 .)( =ν , N ||0=2.1, С1=0.7. The
initial amplitude of the wave is taken so that at 0=r we have
minαα = . This corresponds to cm/kVE 120 = at 0=r .
The ion position at the start and its pitch are identical to the case
when rf is turned off. As the Figs. 4,5 show the ion left the plasma
volume in time less then e/i
Eτ . The principal wave-ion
interaction occurs at the initial and final parts of the ion trajectory.
There is no interaction during the time interval not shown in Fig.5.
The process of the change in the ion kinetic energy is rather
complicated. The initial part of the trace is shown in Fig.6 in more
detail. This period of motion consists of 235 cyclotron periods.
When the ion is moving in the heliotron confining field, the kinetic
energy getting intermits by energy loss or energy conserving (like
from 7 µs to 9 µs). Since V⊥ is the only component of the particle
velocity, that changes its value during heating, the main effect of
heating on guiding center motion is consisted in the change of the
particle pitch (see Fig.7, in which the pitch value, as rf is turned
off, is shown for comparison). The radial component is the main
part of both N⊥ and E⊥ [10]. Therefore, a shift of the particle
guiding center (directed in BE
×⊥ ) occurs mostly in the poloidal
direction. Its value is negligibly small. When the LH power
increases, the time of the ion expulsion becomes shorter (Figs.
8,9), but the kinetic energy increment is increased.
Thus, while simulating the motion of the high energy ions that
initially occupied the region of the “absolute confinement” in a
heliotron, we reveal that these ions can be expelled from plasma
by the LH heating. By making the proper choice of the wave
frequency and initial N || spectrum, it is possible to provide the
wave damping due to the high energy ions only without disturbing
the bulk plasma ions and electrons. Let us refer to the tokamak
experiment [11]. In this experiment the LH heating was applied
during the neutral beam injection (NBI). The growth of ions
perpendicular energy and stimulated ions loss were detected. So,
we conclude that the LH heating can be also used for helium ash
removal in a heliotron-reactor. Now this problem is under
discussion for tokamaks [12,13], but it is also an important
question for heliotrons and stellarators. While applying this
concept to a Heliotron reactor requires detailed simulation of the
expelled particles motion outside the last closed flux surface. The
ion energy of 100 keV, taken in our simulations as an example, is
close to the energy of NB injected ions in LHD [14]. Thus, it is
possible to check the method suggested in the paper, performing
the proper experiment in this heliotron. Being performed, this
experiment should be accompanied by the calculations of the
antenna spectrum, the LH wave propagation and absorption and
the estimation of the required power.
REFERENCES
1. A. Iiyoshi et al., Fusion Technol. 17, 169 (1990).
2. J. Todoroki, J. Phys. Soc. Jpn 59, 2758 (1990).
3. K. N. Sato et al., Nucl. Fusion 35, 1563 (1995).
4. J.E.Stevens et al., Heating in Toroidal Plasmas, Proc. of the 3rd
Joint Varenna-Grenoble Int. Symp., Grenoble, 1982, ) 2, 455.
5. M.Porkolab, J.J.Shuss, Y.Takase et al., ibid, 469.
6. C.F.F.Karney, Phys.Fluids 21, 1584 (1978).
7. C.F.F.Karney, Phys.Fluids 22, 2188 (1979).
8. A. H. Boozer, Phys. Fluids 27, 2441 (1984).
9. A. H. Boozer, Phys. Fluids 23, 904 (1980).
10. D.L.Grekov et al., Nuclear Fusion 30, 2039 (1990).
11. A.H.Kritz et al. Bull. Amer. Phys. Soc. 22, 1170 (1977).
22
12. H.E.Mynick, Phys. Fluids B 5, 2460 (1993).
13. H.E.Mynick and N.Pomphrey, Nuclear Fusion 34, 1277
(1994).
14. M.Fujiwara et al., Plasma Phys. and Contr. Fusion 41,
Suppl.12B, B157 (1999).
FIGURES
- 1 . 0 - 0 . 5 0 . 0 0 . 5 1 . 0
0
1 5
1 0 0
λ
E
E> 3 τ i / e
τ i / e
t i c
Fig.1. A variation of the particle confinement time tic via pitch.
The start point r=a p /2, θ0=π/6, φ0=0
-20
0
20
360 380 400
↓
R(cm)
Z(
cm
)
Fig.2. The absolutely confined passing ion orbit, started (arrow)
from the outside of the torus with r=a p /2, θ0=π/6, φ0=0 and
λ=0.6 is shown. Here the distance from trace to magnetic axis
(Z=0 cm, R=375 cm) corresponds to current average radius of
flux surface. The rf heating is turned off. The particle drift is
directed inside the initial flux surface
0.4 0.5 0.6 0.7
0.35
0.40
0.45
λ
t(ms)
Fig.3. A variation of the pitch λ via time is shown during a drift
for the passing particle orbit (Fig.2)
330 360 390 420
-60
-30
0
30
60
↓
Z(
cm
)
R(cm)
Fig.4. As in Fig. 2, but rf is turned on. The particle becomes
trapped in the helical ripple well, which leads to the change in the
direction of the particle drift and its escape from the plasma
0.0 0.1 0.7 0.8
100
150
200
250
300
W(keV)
t(ms)
Fig.5. A variation of W via time is shown during a drift for the
particle orbit presented in Fig.4
0 2 4 6 8 10
100
120
140 W(keV)
t(µ s)
Fig.6. A variation of W via time is shown in more detail for the
initial part of trace presented in Fig.4
0 2 4 6 8 10
0.52
0.56
0.60
0.64
λ
t(µ s)
Fig.7. A variation of the pitch λ via time is shown for the same
period as in Fig.6. The squares correspond to rf is turned and
open circles relate to rf is turned off
330 360 390 420
-60
-30
0
30
60
→
Z
(c
m
)
R(cm)
Fig.8. As in Fig.4, but LH wave amplitude is doubled
0.00 0.07 0.14 0.21
100
200
300
400
W(keV)
t(ms)
Fig.9. A variation of W via time is shown during a drift for the
particle orbit presented in Fig.8
23
REFERENCES
figures
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