Plasma flow equilibrium, confinement scaling laws and fusion prospects of a field reversed configuration
Field reversed configuration (FRC) is a prospective high b magnetic system for high efficiency D–³He fusion reactor. Self-consistent FRC plasma profiles and static electric field for reactor calculations are discussed in framework of the model including flow equilibrium and collisionless transport e...
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| Zitieren: | Plasma flow equilibrium, confinement scaling laws and fusion prospects of a field reversed configuration / A.Yu. Chirkov // Вопросы атомной науки и техники. — 2007. — № 1. — С. 55-57. — Бібліогр.: 17 назв. — англ. |
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Chirkov, A.Yu. 2017-01-04T08:24:07Z 2017-01-04T08:24:07Z 2007 Plasma flow equilibrium, confinement scaling laws and fusion prospects of a field reversed configuration / A.Yu. Chirkov // Вопросы атомной науки и техники. — 2007. — № 1. — С. 55-57. — Бібліогр.: 17 назв. — англ. 1562-6016 PACS: 52.30.-q; 52.30.Ex; 52.55.Lf; 28.52.-s; 52.55.Dy https://nasplib.isofts.kiev.ua/handle/123456789/110384 Field reversed configuration (FRC) is a prospective high b magnetic system for high efficiency D–³He fusion reactor. Self-consistent FRC plasma profiles and static electric field for reactor calculations are discussed in framework of the model including flow equilibrium and collisionless transport equations. The extrapolations to reactor regimes of plasma confinement scaling laws are considered. Звернена магнітна конфігурація (FRC), – магнітна пастка з високим b, є перспективною системою для високоефективного D–³He-термоядерного реактора. Самоузгоджені розподіли параметрів плазми FRC і статичного електричного поля для розрахунків реактора обговорюються в рамках моделі, що включає рівняння рівноваги течій і беззіштовхувального переносу. Розглядається екстраполяція скейлінгів для утримання плазми в область реакторних режимів. Обращенная магнитная конфигурация (FRC), – магнитная ловушка с высоким b, является перспективной системой для высокоэффективного D–³He-термоядерного реактора. Самосогласованные распределения параметров плазмы FRC и статического электрического поля для расчетов реактора обсуждаются в рамках модели, включающей уравнения равновесия течений и бесстолкновительного переноса. Рассматривается экстраполяция скейлингов для удержания плазмы в область реакторных режимов. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Basic plasma physics Plasma flow equilibrium, confinement scaling laws and fusion prospects of a field reversed configuration Рівновага течій плазми, закони утримання і термоядерні перспективи зверненої магнітної конфігурації Равновесие течений плазмы, законы удержания и термоядерные перспективы обращенной магнитной конфигурации Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Plasma flow equilibrium, confinement scaling laws and fusion prospects of a field reversed configuration |
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Plasma flow equilibrium, confinement scaling laws and fusion prospects of a field reversed configuration Chirkov, A.Yu. Basic plasma physics |
| title_short |
Plasma flow equilibrium, confinement scaling laws and fusion prospects of a field reversed configuration |
| title_full |
Plasma flow equilibrium, confinement scaling laws and fusion prospects of a field reversed configuration |
| title_fullStr |
Plasma flow equilibrium, confinement scaling laws and fusion prospects of a field reversed configuration |
| title_full_unstemmed |
Plasma flow equilibrium, confinement scaling laws and fusion prospects of a field reversed configuration |
| title_sort |
plasma flow equilibrium, confinement scaling laws and fusion prospects of a field reversed configuration |
| author |
Chirkov, A.Yu. |
| author_facet |
Chirkov, A.Yu. |
| topic |
Basic plasma physics |
| topic_facet |
Basic plasma physics |
| publishDate |
2007 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Рівновага течій плазми, закони утримання і термоядерні перспективи зверненої магнітної конфігурації Равновесие течений плазмы, законы удержания и термоядерные перспективы обращенной магнитной конфигурации |
| description |
Field reversed configuration (FRC) is a prospective high b magnetic system for high efficiency D–³He fusion reactor. Self-consistent FRC plasma profiles and static electric field for reactor calculations are discussed in framework of the model including flow equilibrium and collisionless transport equations. The extrapolations to reactor regimes of plasma confinement scaling laws are considered.
Звернена магнітна конфігурація (FRC), – магнітна пастка з високим b, є перспективною системою для високоефективного D–³He-термоядерного реактора. Самоузгоджені розподіли параметрів плазми FRC і статичного електричного поля для розрахунків реактора обговорюються в рамках моделі, що включає рівняння рівноваги течій і беззіштовхувального переносу. Розглядається екстраполяція скейлінгів для утримання плазми в область реакторних режимів.
Обращенная магнитная конфигурация (FRC), – магнитная ловушка с высоким b, является перспективной системой для высокоэффективного D–³He-термоядерного реактора. Самосогласованные распределения параметров плазмы FRC и статического электрического поля для расчетов реактора обсуждаются в рамках модели, включающей уравнения равновесия течений и бесстолкновительного переноса. Рассматривается экстраполяция скейлингов для удержания плазмы в область реакторных режимов.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/110384 |
| citation_txt |
Plasma flow equilibrium, confinement scaling laws and fusion prospects of a field reversed configuration / A.Yu. Chirkov // Вопросы атомной науки и техники. — 2007. — № 1. — С. 55-57. — Бібліогр.: 17 назв. — англ. |
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2025-11-24T02:18:23Z |
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2025-11-24T02:18:23Z |
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| fulltext |
Problems of Atomic Science and Technology. 2007, 1. Series: Plasma Physics (13), p. 55-57 55
PLASMA FLOW EQUILIBRIUM, CONFINEMENT SCALING LAWS
AND FUSION PROSPECTS OF A FIELD REVERSED CONFIGURATION
A.Yu. Chirkov
Bauman Moscow State Technical University,
2nd Baumanskaya Str. 5, 105005, Moscow, Russia, e-mail: chirkov@power.bmstu.ru
Field reversed configuration (FRC) is a prospective high β magnetic system for high efficiency D–3He fusion
reactor. Self-consistent FRC plasma profiles and static electric field for reactor calculations are discussed in framework
of the model including flow equilibrium and collisionless transport equations. The extrapolations to reactor regimes of
plasma confinement scaling laws are considered.
PACS: 52.30.-q; 52.30.Ex; 52.55.Lf; 28.52.-s; 52.55.Dy
1. INTRODUCTION
The field reversed magnetic configuration (FRC) is
the cylindrical magnetic trap with high β (β is the ratio of
plasma pressure to magnetic field pressure). In FRC
plasma is confined in the region of the closed force lines
of the magnetic field. Magnetic field in FRC plasma is
generated both exterior magnetic coils and a diamagnetic
current. Plasma places around of a neutral layer (or a
neutral line) where pressure of plasma has a maximum,
magnetic field B=0 and β=1. Closed lines area is bounded
by the separatrix. According terminology of toroidal
systems FRC has a high elongation, and it’s aspect ratio
equal to unity. Usually magnetic field in the FRC is
supposed to be pure poloidal, but FRC equilibriua with
small toroidal component are possible [1].
One of the important problems of present FRCs is
high anomalous transport across magnetic field. In the
present paper possible confinement scaling laws are
discussed and compared with reported data of
experiments [2–8]. One can suppose that L-mode was
realized in mentioned experiments. Note that H-mode
formation has led to improvement of a plasma lifetime in
reversed field pinch (RFP) [9].
High β values allow consider FRC as a base for high
efficiency D–3He fusion reactor. The main goal of this
work is physical justification of D–3He reactor based on
FRC. To estimate confinement time for H-mode reactor
operation regimes we modify L-mode confinement
scaling laws taking into account anomalous transport
suppression by flow shear. To calculate flow velocities,
static electric field, plasma density and temperature
profiles we use self-consistent model of plasma
equilibrium with flows and transport [10]. In this model
thermodynamic approach to flow invariants is similar to
the model of two-fluid equilibria with flows [1].
FRC reactor parameters are calculated from power
balance of high-β D–3He fusion plasma [11, 12]. We also
compare D–3He FRC reactor concept with D–3He
spherical tokamak [13].
2. FLOW EQUILIBRIUM CALCULATIONS
System of equations of flow equilibrium with
turbulent transport [10] includes diffusion and energy
equations associated with thermodynamic and Maxwell
equation. The key equation of this system for “j”
component (j = i, e) of the plasma is
)(
2
1 2
jjj
jj
jB
j
j hUq
m
Tk ψ
η
η
=++
+ u
, (1)
where jjj nT ∇∇= /η ; kB is the Boltzmann constant; Tj,
nj, and uj are temperature, density and flow velocity; mj
and qj are the mass and the charge of the particle; U is the
potential of the static electric field; hj(ψj) is the surface
function of so-called adiabatic surface; ψj is the flux
function of the adiabatic surface. Using this model we
estimate the maximal ion flow shear parameter as
)/( 2
shear BbqTk iiB≈γ , (2)
where b is the width of flow shear region.
3. CONFINEMENT TIME SCALING LAWS
3.1. L-MODE
Recently good agreement of low-frequency drift wave
scaling laws [14] with experimental data [2–8] was
shown. Confinement time also can be estimated using the
results of calculations of the electrostatic finite β ITG-like
instability driven by non-adiabatic particles and magnetic
force line curvature [15].
Let’s consider “universal” scaling for L-mode particle
confinement time in form
t
0
2
1
2
Tk
eBaaC
B
C
T
L
=
ρ
τ , (3)
where C1 and C2 are some constants, a is the separatrix
radius, )/( 0t eBTkm BiT =ρ , e is the electron charge,
B0 is the external coil magnetic field (vacuum value),
ei TTT +=t is so-called total temperature.
In limiting case C2 = 0 (or C2 = 1) Eq. 3 corresponds
to Bohm (or gyro-Bohm) scaling.
mailto:chirkov@power.bmstu.ru
56
10 100 1000
10
100
1000
τexp
(µs)
τgyro-Bohm∝a3B0
2Tt
-3/2 (µs)
Fig. 1. Comparison of gyro-Bohm scaling with
experimental data
For example, gyro-Bohm scaling (in usual SI units
exclude Tt in eV) is 2/3
t
2
0
33
Bohmgyro 104 −
− ×= TBaτ . The
comparisons of particle confinement time values
measured in experiments [2–8] τexp with the gyro-Bohm
scaling are presented in Fig. 1. Note for Bohm scaling
with C1≈10 [16] agreement with experimental data not
worse than for gyro-Bohm one.
3.2. H-MODE EXTRAPOLATION
Taking into account turbulence suppression by flow
shear [17] one can write confinement time
)1( 22
shear cL τγττ += , (4)
where τc is the turbulence correlation time having an
order of inverse linear instability increment. Correlation
time can be estimated from the overage diffusivity for L-
mode (D⊥L) as follows
LLc aD ττδ // 22 ≈≈ ⊥ , (5)
where δ ≈ b is the width of the turbulent layer near FRC
separatrix.
So, extrapolation of the confinement time to reactor
H-mode is 32
shear
2)/( LL a τγδττ += . For high efficiency
reactor strong flow shear is needed: γshear>>τL
–1, τ >>τL,
32
shear
2)/( La τγδτ ≈ . Let’s consider the most pessimistic
L-mode scenario with Bohm confinement time scaling
law )/(10 t0
2
Bohm TkeBa BL == ττ . In this case for
reactor calculation we use extrapolation in form
+=
4
22
t
0
2
100110
b
a
Tk
eBa
B
δ
τ . (6)
Also for reactor configuration we assume δ ≈ b ≈ 0.1a.
β
r/a
Fig. 2. Plasma β profile for reactor calculations
P, MW/m3
r, m
1
2
3
4
5
Fig. 3. Power distributions. 1 – fusion power, 2 – neutron
power, 3 – bremsstrahlung, 4 – emitted synchrotron
radiation power, 5 – synchrotron radiation taking into
account absorption
4. FUSION PLASMA POWER BALANCE AND
FRC REACTOR CONCEPT
For FRC reactor plasma we consider temperature and
density profiles connected as follows ηnT ∝ with η = 2
and Te = Ti. Corresponding β profile is plotted in Fig. 2.
D–3He fusion plasma and FRC reactor parameters we
calculate using models of D–3He fuel cycles [11] and
FRC fusion plasma [12]. These models are based on
integral power balance
∫
Σ
+++=
+
V
jBj dV
Tkn
PPPP
Q τsbrnfus
11 , (7)
where Q is the plasma power amplification factor; Pfus,
Pn, Pbr and Ps are fusion power, neutron power,
bremsstrahlung power and synchrotron radiation power
integrated over plasma volume V.
In Fig. 3 radial power distributions for D–3He FRC
fusion reactor are plotted. Results of calculations are
presented in the Table. For comparison Table contains
parameters of D–3He spherical tokamak reactor [13].
57
Parameters of D–3He reactors based on FRC and spherical tokamak for regimes with Q=20
Reactor type FRC Spherical tokamak [13]
Fuel cycle D–3He, n3He/nD=1 D–3He with 3He self-supply,
n3He/nD=0.36
Plasma radius a, m 1.6 3
Aspect ratio 1 1.5
Elongation – 3.8
Magnetic field B0, T 5 3.2
Maximal/averaged β 1/0.46 0.95/0.54
Maximal/averaged T, keV 60/28 50/40
Synchrotron wall reflectivity Γs 0.5 0.65
Confinement time τ, s (scaling) 2.5 (Eq. (6)) 16 (ITER)
Fusion power Pfus, MW 32.3 per meter
of plasma cylinder
1500
Bremsstrahlung power fraction Pbr/Pfus 0.4 0.6
Synchrotron power fraction Ps/Pfus 0.052 0.023
Neutron power fraction Pn/Pfus 0.072 0.15
Neutron wall load Wn, MW/m2 0.18 0.2
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14. A.Yu. Chirkov // Prikl. Fiz. (submitted) (in Russian).
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