Confinement physics of helical plasmas versus tokamaks
The comparative studies of plasma confinement properties of helical and tokamak systems are carried out. Global core confinement scaling laws of both systems are similar and gyro-Bohm-like. However, local transport process is different due to inherent transport barrier and neoclassical helical rippl...
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irk-123456789-802662015-04-15T03:02:02Z Confinement physics of helical plasmas versus tokamaks Yamazaki, K. Kikuchi, M. Magnetic confinement The comparative studies of plasma confinement properties of helical and tokamak systems are carried out. Global core confinement scaling laws of both systems are similar and gyro-Bohm-like. However, local transport process is different due to inherent transport barrier and neoclassical helical ripple transport loss. As for stability limits, achievable beta in tokamak is explained by ideal or resistive MHD theories. On the other hand, beta values obtained so far in helical systems are beyond ideal Mercier mode limits. Density limits in tokamaks are often related to the coupling between radiation collapse and disruptive MHD instabilities, but the slow radiation collapse is dominant in the helical system. The pulse length of both tokamak and helical systems is on the order of hours in small machines, and the longer-pulsed good-confinement plasma operations compatible with radiative divertors are anticipated in both systems in the future. For a future advanced reactor, both tokamak and helical systems should be complementary developed. 2002 Article Confinement physics of helical plasmas versus tokamaks / K. Yamazaki, M. Kikuchi // Вопросы атомной науки и техники. — 2002. — № 4. — С. 3-7. — Бібліогр.: 19 назв. — англ. 1562-6016 PACS: 52.55Hc; 52.55Fa http://dspace.nbuv.gov.ua/handle/123456789/80266 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Magnetic confinement Magnetic confinement Yamazaki, K. Kikuchi, M. Confinement physics of helical plasmas versus tokamaks Вопросы атомной науки и техники |
| description |
The comparative studies of plasma confinement properties of helical and tokamak systems are carried out. Global core confinement scaling laws of both systems are similar and gyro-Bohm-like. However, local transport process is different due to inherent transport barrier and neoclassical helical ripple transport loss. As for stability limits, achievable beta in tokamak is explained by ideal or resistive MHD theories. On the other hand, beta values obtained so far in helical systems are beyond ideal Mercier mode limits. Density limits in tokamaks are often related to the coupling between radiation collapse and disruptive MHD instabilities, but the slow radiation collapse is dominant in the helical system. The pulse length of both tokamak and helical systems is on the order of hours in small machines, and the longer-pulsed good-confinement plasma operations compatible with radiative divertors are anticipated in both systems in the future. For a future advanced reactor, both tokamak and helical systems should be complementary developed. |
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Article |
| author |
Yamazaki, K. Kikuchi, M. |
| author_facet |
Yamazaki, K. Kikuchi, M. |
| author_sort |
Yamazaki, K. |
| title |
Confinement physics of helical plasmas versus tokamaks |
| title_short |
Confinement physics of helical plasmas versus tokamaks |
| title_full |
Confinement physics of helical plasmas versus tokamaks |
| title_fullStr |
Confinement physics of helical plasmas versus tokamaks |
| title_full_unstemmed |
Confinement physics of helical plasmas versus tokamaks |
| title_sort |
confinement physics of helical plasmas versus tokamaks |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2002 |
| topic_facet |
Magnetic confinement |
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http://dspace.nbuv.gov.ua/handle/123456789/80266 |
| citation_txt |
Confinement physics of helical plasmas versus tokamaks / K. Yamazaki, M. Kikuchi // Вопросы атомной науки и техники. — 2002. — № 4. — С. 3-7. — Бібліогр.: 19 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT yamazakik confinementphysicsofhelicalplasmasversustokamaks AT kikuchim confinementphysicsofhelicalplasmasversustokamaks |
| first_indexed |
2025-07-06T04:14:05Z |
| last_indexed |
2025-07-06T04:14:05Z |
| _version_ |
1836869480634908672 |
| fulltext |
MAGNETIC CONFINEMENT
Problems of Atomic Science and Technology. 2002. 4. Series: Plasma Physics (7). P. 3-7 3
CONFINEMENT PHYSICS OF HELICAL PLASMAS VERSUS TOKAMAKS
Kozo Yamazakia and Mitsuru Kikuchib
a) National Institute for Fusion Science, Toki, Gifu 509-5292, Japan
b) Japan Atomic Energy Research Institute, Naka, Ibaraki 311-0193, Japan
The comparative studies of plasma confinement properties of helical and tokamak systems are carried out. Global
core confinement scaling laws of both systems are similar and gyro-Bohm-like. However, local transport process is
different due to inherent transport barrier and neoclassical helical ripple transport loss. As for stability limits, achievable
beta in tokamak is explained by ideal or resistive MHD theories. On the other hand, beta values obtained so far in
helical systems are beyond ideal Mercier mode limits. Density limits in tokamaks are often related to the coupling
between radiation collapse and disruptive MHD instabilities, but the slow radiation collapse is dominant in the helical
system. The pulse length of both tokamak and helical systems is on the order of hours in small machines, and the
longer-pulsed good-confinement plasma operations compatible with radiative divertors are anticipated in both systems
in the future. For a future advanced reactor, both tokamak and helical systems should be complementary developed.
PACS: 52.55Hc; 52.55Fa
1. INTRODUCTION
For the realization of attractive fusion reactors, higher-
performance confinement and longer-pulsed operations
should be achieved in addition to the demonstration of
ignited plasma productions. The burning plasma physics
and engineering system integration are explored by ITER
[1] and wide range of plasma operations will be carried
out by using more advanced toroidal systems such as
advanced tokamak and helical systems. There are several
plasma operational limits: (1) confinement limit, (2)
stability limit, (3) density limit, and (4) pulse-length limit.
Here we would like to discuss on toroidal plasma
confinement properties focusing on the similarities and
differences between helical and tokamak systems.
Physics for plasma operational boundaries should be
clarified, and be extended to the higher performance limit.
A comprehensive comparison has been done by Prof.
Wagner [2] by using L-mode tokamak database and
medium-sized stellarator database. These comparisons
have recently been updated [3] using Elmy H-mode
tokamak database and helical confinement database
including recent LHD data [4].
2. HELICAL/TOKAMAK ACHIEVED
PLASMA PARAMETERS
The maximum plasma parameters obtained in tokamak
and helical systems are summarized in Table I. The
highest parameters of tokamak plasmas were obtained in
various machines such as JT-60U (highest temperature,
highest fusion triple product), JET (longest confinement
time and highest stored energy), DIII-D (highest beta),
Alcator-C (highest density) and TRIAM-1M (longest
duration); on the other hand a number of helical machines
is still small and the Large Helical Device (LHD)
produces almost all highest parameters. At present, there
is still a parameter gap between tokamak and helical
systems.
Not only absolute parameters, but also normalized
parameters are very important for the extrapolation of the
present database to the future reactor. Figure 1 shows the
operational domain for present machines and tokamak
reactor SSTR [5], LHD-type helical reactors MHR [6], by
using normalized parameters such as normalized gyro-
radius, plasma beta value and collisionality:
)/(~/
/~/
)/(~/
22/5
*
22
*
Tnaa
BnTBnkT
aBTa
thei
s
εννν
β
ρρ
=
=
=
The tokamak data used here are the Elmy H-mode
database (IPB-DB3v5) [1] and data from JT-60U
advanced tokamak operation [7], and helical data are the
medium-sized helical machine database [8] in addition to
new LHD data [4,6]. For extrapolation to the reactor, a
few factor reduction in *ρ is required for tokamaks; on
the other hand, the helical system should make access to
the one order of lower *ρ regime in the future. Even in
the present helical database the low collisionality regime
for reactors has been already explored.
3. EQUILIBRIUM PROPERTIES
The standard tokamak is characterized by axi-symmetric
plasma shaping and external plasma current; the standard
helical system is 3-dimensional configuration and net-
current-free operation. These different plasma shapings
give rise to different magnetic confinement properties.
Table I. Achieved Maximum Plasma Parameters
Electron Temperature
Te (keV) 26 (JT-60U) 10 (LHD)
Ion Temperature
Ti (keV) 45 (JT-60U) 5.0 (LHD)
Confinement time
τE (s)
1.2
1.1
(JET)
(JT-60U,NS) 0.36 (LHD)
Fusion Triple Product
ni τE Ti (m
-3 s keV) 15x1020 (JT-60U) 0.22x1020 (LHD)
Stored Energy
Wp (MJ)
17
11
(JET)
(JT-60U,NS) 1.0 (LHD)
Beta Value
β (%)
40 (toroidal)
12 (toroidal)
(START)
(DIII-D) 3.2 (average) (LHD,W7-AS)
Density
ne (1020m-3) 20 (Alcator-C) 3.6 (W7-AS)
Plasma Duration
τdur
2 min
3 hr. 10min.
(Tore-Supra)
(Triam-1M)
2 min
1 hour
(LHD)
(ATF)
TOKAMAK HELICAL
4
Example of rotational transform for tokamak and
helical systems is shown in Fig. 2. In tokamak systems,
magnetic shear is easily modified by the plasma current
distribution, for example normal shear discharges and
current hole discharges in JT-60U [9]. These shear
profiles make strong effect on the production of
confinement improvement modes. On the other hand, a
variety of magnetic shear configurations can be produced
by choosing helical coil systems. The q-profile is reversed
or flat, and the magnetic hill region exists near the plasma
edge in the conventional helical system.
The divertor configurations strongly depend on the
plasma shape. The 2-dimentional tokamak system has
poloidal divertor with remote radiation. In helical
systems, helical divertor concept with rather large divertor
space is adopted in LHD. In the design of modular helical
systems the island divertor concept is explored and its
effectiveness is demonstrated [10]. The divertor and
scrape off layer are related to ergodicity and magnetic
island, and differences in stochastic magnetic layers give
rise to differences in the performance of plasma
confinement.
At present, various advanced plasma shapings for helical
systems are proposed. Some of them are sorts of tokamak-
helical hybrid aiming at disruption-free steady-state
operations.
4. HELICAL/TOKAMAK PLASMA
CONFINEMENT
The global plasma confinement scaling laws in tokamak
and helical plasmas are well established, Elmy H-mode
IPB98(y) [1] for tokamak and ISS95 for helical systems
[8];
97.023.008.041.063.093.10365.0 IBnPR e
ELMY
E ετ −= (1)
95 2.21 0.65 0.59 0.51 0.80 0.40
2 / 30.079ISS
E ea R P n Bτ ι−= (2)
Where R, a, P, en ,B,ε , 3/2ι are major radius (unit: m),
minor radius (m), heating power (MW), line-averaged
density (1019/m3), inverse aspect ratio, and rotational
transform at ρ =2/3 in helical systems. These two scaling
laws are shown in Fig. 3. To compare database of
tokamak and helical systems, we used the simple formula
of equivalent plasma current Iequiv with average minor
radius aav for helical systems:
)()(
)()(51
)()(
)()(2/)1(
5
2
3/2
22
MAImR
TBma
MAImR
TBma
RB
aBq
equiv
tav
P
t
p
t =≡
+
==
ι
κ (3)
Figure 3 also shows a comparison between tokamak
confinement and helical confinement using ELMY
Eτ
and 95ISS
Eτ . The tokamak data scaled by using both
confinement laws seem better than the scaled medium-
sized helical data, however, the LHD data stays on the
ITER Elmy H mode scaling using the above equivalent
plasma current. Globally, tokamak and helical transports
look similar and of gyro-Bohm type,
0.83 0.50 0.10
* *
ELMY
E Bτ τ ρ β ν− − −∝ ,
0.01
0.1
1
10
<b
et
a>
.001 .01 .1
<rho>
ASDEX
AUG
CMOD
COMPASS
D3D
JET
JFT2M
JT60U
PBXM
PDX
TCV
TOK
d‚ ‡‚ g
0.001
0.01
0.1
1
10
100
<n
u>
.001 .01 .1
<rho>
ASDEX
AUG
CMOD
COMPASS
D3D
JET
JFT2M
JT60U
PBXM
PDX
TCV
TOK
d‚ ‡‚ g
0.01
0.1
1
10
<b
et
a>
.001 .01 .1
<rho>
ATF
CHS
FFHR
HELE
HSR
LHD
MHR
SPPS
W7-A
W7-AS
STELL
d‚ ‡‚ g
0.001
0.01
0.1
1
10
100
<n
u>
.001 .01 .1
<rho>
ATF
CHS
FFHR
HELE
HSR
LHD
MHR
SPPS
W7-A
W7-AS
STELL
d‚ ‡‚ g
*ρ
β
*ρ
*ν
*ν
SSTR
SSTR
MHR
MHR
HELICALTOKAMAK
*ρ *ρ
β
LHD high-beta
DIII-D high-beta
Fig. 1. Dimensionless operational regimes in tokamak and helical existing machines
and future reactors (SSTR,MHR).
0
0.5
1
1.5
2
0 0.2 0.4 0.6 0.8 1
1/q
rho
TJ-II
LHD
JT-60U Normal Shear
W7-AS
JT-60U Current Hole
0
0.5
1
1.5
2
0 0.2 0.4 0.6 0.8 1
1/q
rho
0
0.5
1
1.5
2
0 0.2 0.4 0.6 0.8 1
1/q
rho
TJ-II
LHD
JT-60U Normal Shear
W7-AS
JT-60U Current Hole
Fig. 2. Magnetic rotational transform of tokamak
and helical systems.
5
95 0.71 0.16 0.04
* *
ISS
E Bτ τ ρ β ν− − −∝ ,
but local transport seems different. The standard tokamak
confinement near the center is determined by sawteeth
oscillations, and helical core confinement is affected by
helical ripple loss especially in the high temperature and
low density regime.
The local transport, especially, the internal transport
barrier (ITB) looks different between tokamak and helical
systems. The tokamak has clear internal transport barrier
on electron and ion thermal transports as obtained in JT-
60U experiments. The radial electric field shear is driven
by toroidal rotation and pressure gradient. On the other
hand, in helical system, radial electric field is driven by
ripple loss predicted by neo-classical transport theory. In
the low density regime the neo-classical ITB near the
plasma center was obtained by the appearance of positive
electric field in CHS [11]. The same phenomena have
recently been observed in LHD and the detailed physics
will be clarified in the future [12].
5. HELICAL/TOKAMAK STABILITY LIMITS
In tokamak systems ideal beta limits agree with ideal
MHD theory, and global beta scaling law is given by
5.3
)/(
(%)
≤≡
tp
N aBI
β
β (4)
The pressure peaking effects on plasma stability are also
explained by the ideal MHD theory. Moreover, the
resistive beta limits agree with neoclassical tearing mode
(NTM) or classical tearing mode (CTM) and resistive
wall mode (RWM). The kink-ballooning modes, which
are current driven mode coupled with pressure driven
mode, are restrictive in tokamak discharges. There is a
good agreement between experimental data and
theoretical analysis in JT-60U [13]. On the other hand, in
helical system pressure driven modes are dominant. In the
LHD experiment, achieved beta value is beyond the
Mercier local mode theory, while the global mode
analyzed by Terpschore code [14] is still marginal.
PBX-M
T-11JT-60U
TFTR
ASDEX
ITER
DIII-D
DIII-D
1 2 30
2
4
6
8
10
12
βN
=3
.5
Stability
Normalized current I/aB (MA/m/T)
Tokamak Helical
Ideal beta agrees
with Ideal MHD
Resistive beta
agrees with NTM &
TM, RWM theories
Beta
obtained
beyond
Mercier
mode
Global
mode is
still
marginal.
3.6 3.7 3.8 3.9
R(m)
Equilibrium Limit
Stability
Limit
0
2
4
6
Beta
(%)
LHD Exp.
Optimized Reactor
Magnetic Well
Good Particle Orbit
Fig.4. Access to high beta in tokamak and helical (LHD) system.
0.001
0.01
0.1
1
10
ta
u_
ex
p
.001 .01 .1 1 10
tau_IPB98(y)
ATF
CHS
FFHR
HELE
HSR
LHD
MHR
SPPS
W7-A
W7-AS
STELL
d‚ ‡‚ g
0.001
0.01
0.1
1
10
TA
U
TO
T
.001 .01 .1 1 10
IPB98(y)
ASDEX
AUG
CMOD
COMPASS
D3D
JET
JFT2M
JT60U
PBXM
PDX
TCV
TOK
d‚ ‡‚ g
0.001
0.01
0.1
1
10
TA
U
TO
T
.001 .01 .1 1 10
tau_ISS
ASDEX
AUG
CMOD
COMPASS
D3D
JET
JFT2M
JT60U
PBXM
PDX
TCV
TOK
d‚ ‡‚ g
0.001
0.01
0.1
1
10
ta
u_
ex
p
.001 .01 .1 1 10
tau_ISS95
ATF
CHS
FFHR
HELE
HSR
LHD
MHR
SPPS
W7-A
W7-AS
STELL
d‚ ‡‚ g
95ISS
Eτ
10.050.083.0 ** −−−∝ νβρττ B
ELMY
E
04.016.071.095 ** −−−∝ νβρττ B
ISS
E
EXP
Eτ
EXP
Eτ EXP
Eτ
EXP
Eτ
Reactor
Reactor
HELICALTOKAMAK
40.0
3/2
80.051.059.065.021.295 08.0 ιτ BnPRa e
ISS
E
−=
97.023.008.041.063.093.10365.0 IBnPR e
ELMY
E ετ −=
Fig. 3. Confinement scaling laws of tokamak versus helical systems.
Both tokamak (left) and helical (right) data are evaluated by applying tokamak
scaling (upper) and helical scaling (lower) laws.
6
The unstable mode structure is rather broad in tokamak,
on the other hand, the localized mode is crucial in helical
system. The low-n mode has an interchange-like
structure, and the high-n mode has a ballooning-like one.
The current carrying toroidal plasmas are subject to
the existence of conducting wall. The global modes are
easily stabilized by the fitted wall. In helical systems, the
local mode is not linked to the wall, however, the stability
of bootstrap (BS) current-carrying helical systems still
depends on wall position.
6. HELICAL/TOKAMAK DENSITY LIMIT &
RADIATION LOSS
The density limit is mainly related to thermal power
balance and the radiation collapse. In tokamaks the
plasma disruption is often related to the density limits.
The operational density regime is plotted by using
tokamak scaling (Greenwald scaling [15]) and helical
scaling (new scaling with modified coefficient from the
helical scaling [16]).
2_20
m
MA
GR a
In
π
= (5)
⋅= T
mm
MW
mm
TMW
hel B
aR
P
aR
BPMinn 35.0,25.02 2_20
(6)
Figure 5 denotes the density domain of the transport
database used in Figs. 1 & 3, not real density limits. This
helical scaling can roughly fit to tokamak data as shown
in this figure. The density limit of helical plasmas does
not seem to be related to the magnetic rotational
transform, which is different from the tokamak density
limits. The radiation collapse in tokamaks often gives rise
to plasma current quench; the helical high-density
collapse leads to slow plasma decay.
To produce disruption-free tokamak discharges, one of
possible methods is to add external helical field to
tokamak plasmas. The complete suppression of major
disruption by applying external rotational
transform 14.0≥ι had been demonstrated in W7A [17] and
JIPP T-II stellarator [18] twenty years ago. We should
check experimentally whether this method is effective
even in the BS driven tokamaks.
7. HELICAL/TOKAMAK STEADY-STATE
OPERATION
The longest pulsed operation is demonstrated in the
TRIAM-1M tokamak for 3 hours and 10minuts [19]. The
long-pulsed higher performance discharges are carried out
in Tore-Supra. The reactor requirement in steady-state
tokamaks is to utilize BS currents and to reduce the
circulation power of the reactor plant. The full non-
inductive operation with 80% BS current fractions and
20% beam driven current has been demonstrated in JT-
60U [7].
In helical system, it is easy to keep its magnetic
configuration in steady state, and the remained issue is to
check compatibility between divertor and plasma
confinement.
8. SUMMARY
We can summarize the operational limits of tokamak
and helical plasmas in Table II. The magnetic
configuration in tokamak system can be easily changed by
modifying plasma current distribution; in helical systems
various plasma shapings by adopting the helical coil
system give rise to a variety of magnetic properties. Both
global confinement properties are same such as gyro-
Bohm scaling. However, local transport is not similar
between tokamak and helical system, especially radial
electric field formation and internal transport barrier
(ITB) properties. The plasma stability of tokamak might
be determined by MHD theory related to current driven
and pressure driven modes; in helical system the pressure-
driven mode is dominant and the achieved pressure
gradient is beyond Mercier mode limits.
1e+18
1e+19
1e+20
1e+21
N
EB
AR
1e+18 1e+19 1e+20 1e+21
2*ncr
ASDEX
AUG
CMOD
COMPASS
D3D
JET
JFT2M
JT60U
PBXM
PDX
TCV
TOK
d‚ ‡‚ g
1e+18
1e+19
1e+20
1e+21
N
EB
AR
1e+18 1e+19 1e+20 1e+21
nGR
ATF
CHS
HELE
LHD
W7-A
W7-AS
STELL
d‚ ‡‚ g
1e+18
1e+19
1e+20
1e+21
N
EB
AR
1e+18 1e+19 1e+20 1e+21
2*ncr
ATF
CHS
HELE
LHD
W7-A
W7-AS
STELL
d‚ ‡‚ g
1e+18
1e+19
1e+20
1e+21
N
EB
AR
1e+18 1e+19 1e+20 1e+21
nGR
ASDEX
AUG
CMOD
COMPASS
D3D
JET
JFT2M
JT60U
PBXM
PDX
TCV
TOK
d‚ ‡‚ g
radiation collapse
leading to current disruption
radiation collapse
slow plasma decay
HelicalTokamak
LHDn _ LHDn _
GRn _ GRn _
EXPn _
EXPn _
EXPn _
EXPn _
2_20
m
MA
GR a
In
π
=
⋅
=
T
mm
MW
mm
TMW
hel
B
aR
P
aR
BPMin
n
35.0,25.02 2
_20
No dependence
of iota
Fig.5. Operational Density regime plotted by using confinement data-base for tokamak(left)
and helical(right) systems. Tokamak density limit scaling (upper) and helical scaling (lower) are used in both data.
7
The realization of attractive fusion reactors, better
confinement and longer-pulsed operations should be
achieved, in addition to burning plasma physics
clarification that will be performed in ITER [1]. In
tokamak systems, critical issue is to avoid disruption and
to demonstrate steady-state operation; in helical systems
high performance discharges should be demonstrated with
reliable divertor, and compact design concepts should be
explored. Each magnetic confinement concepts should be
developed complementally focusing on above critical
issues keeping their own merits, for realization of
attractive reactors and for clarification of common
toroidal plasma confinement physics.
REFERENCES
[1] ITER Physics Basis Editors et al., Nucl. Fusion 39,
2137 (1999).
[2] F. Wagner, Plasma Phys. Control. Fusion 39, A23
(1997).
[3] K.Yamazaki & M.Kikuchi: “High Performance
Operational Limits of Tokamak and Helical Systems”, J.
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Table II. Operational limits in tokamak
and helical systems
STANDARD TOKAMAK STANDARD HELICAL
Confinement Gyro-Bohm Gyro-Bohm (Global)
Helical Ripple Effect
Beta Limit
Kink-Ballooning Mode
Resistive Wall Mode
Neoclassical Tearing
Low-n Pressure-Driven
Mode
Density Limit Radiation & MHD
Collapses Radiation Collapse
Pulse-Length Limit
Recycling Control
Resistive Wall Mode
Neoclassical Tearing
Recycling Control
Resistive mode (?)
Beyond limit Thermal collapse
Current quench Thermal collapse
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