The behavior of a magnetized plasma under the action of laser with high pulse energy
Simple magnetic traps, such as a cusp and field-reversed configuration are considered for application in high density regime. Magneto-inertial fusion with laser compression of magnetized spherical target and features of laser driven magneto-inertial fusion (LDMIF) are presented. A new fusion scheme...
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irk-123456789-173112011-02-26T12:03:55Z The behavior of a magnetized plasma under the action of laser with high pulse energy Ryzhkov, S.V. Термоядерный синтез (коллективные процессы) Simple magnetic traps, such as a cusp and field-reversed configuration are considered for application in high density regime. Magneto-inertial fusion with laser compression of magnetized spherical target and features of laser driven magneto-inertial fusion (LDMIF) are presented. A new fusion scheme which can avoid some of the major difficulties faced in the present approaches in magnetic and inertial confinement fusion is shown. Different schemes of magnetized discharges for LDMIF are discussed. Contributions (fusion power, charged particles and neutrons deposition, thermal conduction, radiation and mechanical work) to a power balance of compressed plasma target are calculated. Рассмотрен магнитно-инерциальный термоядерный синтез с лазерным драйвером. Представлено моделирование сильно нелинейного режима взаимодействия мощного лазерного импульса с предварительно замагниченной плазмой. В качестве мишеней выбраны магнитные системы удержания плазмы антипробкотрон (касп) и компактный тор (обращенная магнитная конфигурация). Обсуждаются вопросы самосогласованного и внешнего приложенного магнитного поля. Проведен анализ энергетического баланса D-T-плазмы при сферически симметричной имплозии мишени лазером с высокой энергией импульса. Получены основные энергетические характеристики плазменной мишени, вмороженной в магнитное поле. Розглянуто магнітно-інерціальний термоядерний синтез з лазерним драйвером. Представлено моделювання сильно нелінійного режиму взаємодії потужного лазерного імпульсу з попередньо замагніченною плазмою. В якості мішеней вибрано магнітні системи утримання плазми антіпробкотрон (асп) і компактний тор (звернена магнітна конфігурація). Обговорюються питання самоузгодженого і зовнішнього прикладеного магнітного поля. Проведено аналіз енергетичного балансу D-T-плазми при сферично симетричній імплозії мішені лазером з високою енергією імпульсу. Отримано основні енергетичні характеристики плазмової мішені, вмороженої в магнітне поле. 2010 Article The behavior of a magnetized plasma under the action of laser with high pulse energy / S.V. Ryzhkov // Вопросы атомной науки и техники. — 2010. — № 4. — С. 105-110. — Бібліогр.: 29 назв. — англ. 1562-6016 http://dspace.nbuv.gov.ua/handle/123456789/17311 en Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Термоядерный синтез (коллективные процессы) Термоядерный синтез (коллективные процессы) |
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Термоядерный синтез (коллективные процессы) Термоядерный синтез (коллективные процессы) Ryzhkov, S.V. The behavior of a magnetized plasma under the action of laser with high pulse energy |
| description |
Simple magnetic traps, such as a cusp and field-reversed configuration are considered for application in high density regime. Magneto-inertial fusion with laser compression of magnetized spherical target and features of laser driven magneto-inertial fusion (LDMIF) are presented. A new fusion scheme which can avoid some of the major difficulties faced in the present approaches in magnetic and inertial confinement fusion is shown. Different schemes of magnetized discharges for LDMIF are discussed. Contributions (fusion power, charged particles and neutrons deposition, thermal conduction, radiation and mechanical work) to a power balance of compressed plasma target are calculated. |
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| author |
Ryzhkov, S.V. |
| author_facet |
Ryzhkov, S.V. |
| author_sort |
Ryzhkov, S.V. |
| title |
The behavior of a magnetized plasma under the action of laser with high pulse energy |
| title_short |
The behavior of a magnetized plasma under the action of laser with high pulse energy |
| title_full |
The behavior of a magnetized plasma under the action of laser with high pulse energy |
| title_fullStr |
The behavior of a magnetized plasma under the action of laser with high pulse energy |
| title_full_unstemmed |
The behavior of a magnetized plasma under the action of laser with high pulse energy |
| title_sort |
behavior of a magnetized plasma under the action of laser with high pulse energy |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2010 |
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Термоядерный синтез (коллективные процессы) |
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http://dspace.nbuv.gov.ua/handle/123456789/17311 |
| citation_txt |
The behavior of a magnetized plasma under the action of laser with high pulse energy / S.V. Ryzhkov // Вопросы атомной науки и техники. — 2010. — № 4. — С. 105-110. — Бібліогр.: 29 назв. — англ. |
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2025-07-02T18:29:39Z |
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2025-07-02T18:29:39Z |
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1836560919810801664 |
| fulltext |
УДК 533.9
THE BEHAVIOR OF A MAGNETIZED PLASMA UNDER THE ACTION
OF LASER WITH HIGH PULSE ENERGY
S.V. Ryzhkov
Bauman Moscow State Technical University, Moscow, Russia
E-mail: ryzhkov@power.bmstu.ru
Simple magnetic traps, such as a cusp and field-reversed configuration are considered for application in high
density regime. Magneto-inertial fusion with laser compression of magnetized spherical target and features of laser
driven magneto-inertial fusion (LDMIF) are presented. A new fusion scheme which can avoid some of the major
difficulties faced in the present approaches in magnetic and inertial confinement fusion is shown. Different schemes
of magnetized discharges for LDMIF are discussed. Contributions (fusion power, charged particles and neutrons
deposition, thermal conduction, radiation and mechanical work) to a power balance of compressed plasma target are
calculated.
PACS: 52.55.Lf, 52.25.Xz (52.38.Fz, 52.25.Kn)
1. INTRODUCTION
There are two basic principles of thermonuclear
plasma confinement: magnetic and inertial. In the first
case, a dense (10 ...10 m ), high temperature 14 22 -3
(10...20 keV) plasma is kept in a given volume under
the magnetic field pressure, counteracting the plasma
pressure. The second approach is based on the use of
powerful sources of energy, heating of thermonuclear
fuel to high temperatures for a time comparable with the
characteristic times of the hydrodynamic expansion of
the plasma.
Magneto inertial fusion (MIF) is a relatively new
approach [1-3] to producing fusion power that combines
features of the more widely studied magnetic (MCF)
and inertial confinement fusion (ICF). Like the
magnetic approach, the fusion fuel is confined at low
density by magnetic fields while it is heated into a
plasma, but like the inertial approach, fusion is initiated
by rapidly squeezing the target in order to dramatically
increase the density of the fuel, and thus its temperature.
Although the resulting density is much lower than
traditional ICF approaches, it is believed that the
combination of longer confinement times and better
heat retention will allow the MIF approach to provide
the same efficiencies, yet be much easier to build.
___________________________________________________________
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2010. № 4.
Серия: Плазменная электроника и новые методы ускорения (7), с.105-110.
105
Fig.1. Technical implementation of proposed MIF
scheme: 1 – laser beams; 2 - magnetic coils; 3 – target;
4 – discharge system
Typically, in MIF, a magnetized target is com-
pressed by an imploding solid liner [4]. In laser-driven
magneto-inertial fusion (LDMIF), a laser beams with
high energy pulses (laser intensity 10 ...10 W/m15 17 2)
compresses the target [5]. The motivation for this study
is two-fold. First, use this approach to identify possible
LDMIF ignition regions. Second, investigate conditions
in which the laser driver may contribute significantly to
the fusion burn power.
Magnetized cylindrical or spherical targets may be
imploded on laser system to compress a magnetic flux
to multi-megagauss values [6,7]. The experiments [6,8]
demonstrated the bright prospects of laser-driven
inertial confinement fusion with magnetized targets.
The principal scheme of magnetic flux compression
by laser driver is shown in Fig.1. Like in the
experiments [2] the pre-seeded magnetic field can be
easily generated by two high-current loops. MIF dis-
charge system is constructed in [2].
Fuel magnetization and preheat significantly lowers
the required radial convergence enabling cylindrical
implosions to become an attractive path toward generat-
ing fusion conditions. Three potential fusion-based
technologies for MIF are energy production, space pro-
pulsion, and transmutation.
Both MIF and magnetized target fusion (MTF) seeks
to develop magnetically confined, inertially controlled
thermonuclear fusion system (see Fig.1). The main goal
of this paper is modeling of ICF target compression
under laser beams to produce ultrahigh magnetic fields.
Compressed magnetic field will suppress the thermal
transport and lower the ignition requirement.
2
This research is concerned with the compression of
magnetic flux, initially axial in cylindrical geometry by
high β plasmas under ICF conditions. The magnetic
pressure is a small perturbation to the hydrodynamic
pressure in these laser plasmas.
3
Section 2 discusses the concept of laser-driven mag-
netic-flux compression. Magnetic confinement systems
with high β (the ratio of plasma to external magnetic
pressure) for LDMIF are detailed in Sec.3. Analysis of
the power balance is presented in Sec.4. A summary is
discussed in Sec.5.
1 4
mailto:ryzhkov@power.bmstu.ru
Impulse solenoid generates initial
magnetic flux in the target
(magnetized plasma)
Magnetic field is imbedded in the fuel
and laser beams are then accelerated
by driver (external source)
Magnetic flux compression increases
the pressure inside the target, heating it
to ultra-high temperature
Magnetic-flux density is rising, and
allows to generate large magnetic field
(megagauss range)
Fig.2. The implosion scheme – the spherical target compression under laser beams
2. LASER DRIVEN MAGNETIC FLUX
COMPRESSION
By combination of the benefits of magnetic and iner-
tial confinements, a new fusion scheme is introduced
with a dense plasma confined by inertia of laser while
its heat is insulated by a self-generated magnetic field.
Using the ablative pressure of the laser allows to drive a
shell at high implosion velocity, trapping and compress-
ing the external field to magnetize the hotspot center.
Hydrogen may be compressed to more than
10,000 times liquid density by an implosion system en-
ergized by a high energy laser. This scheme makes pos-
sible efficient thermonuclear burn of small pellets of
heavy hydrogen isotopes, and makes feasible fusion
power reactors using practical lasers.
A new fusion scheme which can avoid some of the
major difficulties faced in the present approaches in mag-
netic and inertial confinement fusion is described below.
Interaction of high energy laser pulses with a magnetized
target (Laser Driven Magneto-Inertial Fusion) is shown
schematically on Fig.2. Direct compression of magnet-
ized target in MIF may be divided on 4 stages:
1) The system uses a solenoid operated with a pulsed
voltage power supply to generate initial (pre-seeded)
magnetic field in the imploding target plasma of MIF.
2) The imbedded magnetic field inside the target is
compressed along with the target plasma to achieve
magnetic insulation. Direct compression of the magnet-
ized plasma (target) by laser driver (laser beams).
3) Thus, magnetic field compression leads to increas-
ing of the plasma pressure (dynamic high-pressure on a
target), heating target plasma to ultrahigh temperature.
4) Fuel temperature and pressure both increase to
extremely high values with increasing of compression
ratio, producing ultra-strong magnetic fields in the me-
gagauss range (> 100 T).
Magnetic field amplification during spherical laser
implosion in such scheme may achieve ~ 1000. The
amplification of the magnetic field caused by the implo-
sion are compared in [5]. An amplification factor of
140 seen in the high-explosive data [9] represents a
convergence initial radius divided by the final radius of
12. Laser-driven implosions have an amplification fac-
tor of 560, representing a convergence of 24.
Magnetic-flux compression [10] is a viable path to
generating tens of MG magnetic fields with adequate
size compression of a metal liner [11] driven by high
explosives [9] or by pulsed power. The latter approach
has been pursued by the Z-pinch [12] communities. The
results from the first experiments on a new approach
that provides very effective flux compression are re-
ported here. The field is compressed by the ablative
pressure exerted on an imploding ICF capsule by the
driving laser [2]. This approach was proposed in the
1980s [13] as a way to achieve record compressed fields
with possible applications for fusion [14] but no laser
experiments were performed. There are numerous ad-
vantages to this approach as the implosion velocity is
high (a few 105 m/s) and the hot plasma is an effective
conductor that traps the pre-seeded magnetic field with
minimal resistive diffusion. This approach can be used
to magnetize high-energy-density plasmas for a number
of applications ranging from controlled fusion to labora-
tory astrophysics.
3. SPONTANEOUS AND EXTERNAL
MAGNETIC FIELDS
Self-generated and externally generated magnetic
field imbedded in a plasma are measured in [5,6, 15,16].
The important role played by magnetic fields in laser
plasma is by now universally recognized. However, not-
withstanding the large number of papers published after
first report of registration of the spontaneous magnetic
field, no final conclusion can be drawn concerning the
mechanisms of this phenomenon. The question of genera-
tion of spontaneous magnetic fields in a plasma irradiated
be an electromagnetic field was first investigated in [17].
At present, at least five possible mechanisms for the
generation of the spontaneous magnetic field can be pro-
posed [18, 19]: 1) the flux of charged particles emitted
from the plasma, 2) the charge separation produced when
the plasma interacts with the residual gas, 3) the thermoe-
lectric power produced when ∇T is not parallel to ∇n in
the plasma, 4) the pressure of the light, and 5) the genera-
tion of spontaneous magnetic fields in a plasma acted
upon by high-power electromagnetic radiation. This in-
terest is due primarily to the fact that the resultant strong
magnetic field can greatly influence the character of the
penetration of the light into the plasma and the rate at
which transport phenomena take place in the plasma.
106
The right choice of magnetic configuration is the
most important thing for MIF, so you should first con-
sider the various systems based on the principle of mag-
netic confinement.
Among the various magnetic systems designed for
the containment of a high temperature plasma, the most
promising are closed systems in which the magnetic
field intensity increase towards the periphery. However,
in the great majority cases, the equations for the field
lines of closed systems are non integrable and an
analytical study of the shape of the magnetic field lines,
and even more so an analytical study of the motion of
the charged particles and of plasma behavior in such
fields, does not appear to be a very promising method of
investigation. In any case, when studying containment
problems, the actual detailed disposition of the magnetic
field lines, and the details of the motion of the plasma
inside the system, are not especially interesting. It is
more important to know whether or not the plasma will
remain within the confines of the closed volume.
Antiprobkotron (cusp) [20, 21] and field reversed
configuration (FRC) [22] are axis-symmetric magnetic
systems (Fig.3). The FRC is alternate system with at-
tractive prospects. Preferable choice of plasma con-
finement in magnetic device may be combined with
properties of inertial confinement.
High temperature plasma (target) confined by pol-
oidal magnetic field with taking into account laser sys-
tem (laser driver) to push and compress plasma of com-
pact toroid (CT).
The interacting physical processes involved intro-
duce disparate time scales. For example, the FRC itself
has near-vacuum buffer-field regions that have ex-
tremely high Alfven velocity, while the implosion pro-
ceeds at a much slower pace. These strongly differing
time scales impose stringent accuracy requirements. The
kinetic theory of collisionless heating in FRC type of
magnetized discharge is developed earlier [23].
The compact toroid has the unique aspect of self-
generated magnetic confinement in a closed configura-
tion, requiring only ancillary fields to provide equilib-
rium. Two consequences emerge, the high conductivity
of a fusion temperature plasma allows for slow decay of
the magnetic energy, and the self-contained field con-
figuration allows for CT mobility.
Spherical targets imbedded in a pre-seeded magnetic
field are shown in Fig.3. Magnetic field lines shown by
continuous lines, laser beams - by arrows.
Proposed cusp magnetic field configuration (anti-
probkotron) for laser driven magneto-inertial fusion [24]
may be formed on the base of conventional ICF capsule.
Although the cusp geometry is not now received much
attention in modern magnetic fusion research because of
large losses it can be attractive for fusion applications in
the limit of high intensity magnetic field that can be
generated by laser driven magnetic flux compression.
Before compression
At the instant of the laser impulse maximum
Fig.3. Systems for magnetic flux compression - cusp (antiprobkotron) and FRC (compact toroid)
Oblate (spherical) plasma of FRC is shown on Fig.3.
Insight into compact magnetic confinement systems
formation, confinement and sustainment should help in
the design of future fusion experiments such as the pro-
posed ITER facility. Different applications of compact
systems are very attractive [25]. Right now as neu-
tron/proton source, plasma and materials technology,
plasma-wall interactions, to test face components.
4. POWER BALANCE OF MAGNETIZED
TARGET IN MIF
A power balance in our model includes the power
density deposited by the fusion products pα and pn, pm is
the contribution due to mechanical work, pbr and pe are,
respectively, the power densities lost by radiation
(bremsstrahlung is the main mechanism) and by thermal
conduction.
107
The fraction of the α-particle energy deposited in-
side the considered hot homogeneous sphere of radius R
is given by Krokhin and Rozanov [26] as:
2
3
3 4
, 1 / 2
2 5
1 1
1 ,
2 160
f
α α α
α
α
α α
τ τ τ
τ
τ τ
− ≤
=
− + ≥
⎧
⎪⎪
⎨
⎪
⎪⎩
108
1 / 2
,
where τα = R/lα is the ratio of the radius R of the burning
sphere to the α-particle free path.
Charged α-particles and neutrons interact with the
hot plasma and deposit their energy to the target. The
individual fractions fα and fn are presented in Fig.4 and
6. Fusion power deposited by α-particles within the hot
sphere is shown in Fig.5.
All calculations made for initial density n=10 m 21 -3
and magnetic field B = 2 T. The Coulomb logarithm is
taken 17. Radius range is chosen for conventional ICF
target that may be used for cusp configuration and pre-
formed FRC target.
Fig.4. Fraction associated with α-particles versus
average plasma temperature T and ρR product
Fig.5. Power density associated with α-particles
Considering volume ignition of a large fuel mass the
fractional power deposition for neutrons [27]:
n
n
Rf
R H
ρ
ρ
=
+
,
where ρR is the density-radius product, Hn = 200 kg/m2
is the constant, which applies to a homogeneous D-T-
sphere with uniform neutron source.
The percentage of radiative losses relative to total
loss for MIF is two times lower than in MCF system
because of lower temperature.
fn
ρR,kg/m2Т,keV
Fig.6. Deposition of neutrons from D-T–reaction to the
target compressed by laser beams
PdV work is expansion or compression work due to
plasma pressure and a changing volume, but not related
to the magnetic field (Fig.7). The expression for me-
chanical work in our case may be written as
fα
R
TuR
R
puW DT
m
ρ
33 == ,
where u = 105 m/s is the velocity of the surface of the
sphere (the average velocity of ablation) and RDT = 7.66
x 1010 J/(kg keV) is the gas constant for DT-reaction.
Т,keV ρR,kg/m2
pα , W/m3
Fig.7. Mechanical (PdV) work u = 1 x 105 m/s
pe, W/m3
ρR,kg/m2 Т,keV
Fig.8. Heat loss due to the electronic
thermal conductivity
Т, K R,m
Thermal conductivity suppression by magnetic field
in axial symmetric traps for plasma confinement is
shown both experimentally and theoretically. The pres-
109
ence of a magnetic field decreases both longitudinal and
transversal heat conduction (Fig.8). Applying an exter-
nal magnetic field the thermal conductivity decreases by
several orders of magnitude. And as a result thermal
losses are the lowest part of the energy balance of the
target plasma compared with laser fusion, where the
heat loss may constitute a substantial portion of total
power. The suppressed electronic thermal conductivity
corresponds to a 3-7 fold increase in the plasma tem-
perature and density.
CONCLUSIONS
This study points to solution of problem connected
with theoretical investigation of methods supplying with
magneto inertial fusion (MIF) or magnetized target fu-
sion (MTF) plasma [28].
Magneto-inertial approach to a fusion combines the
advantages of magnetic and inertial confinement fusions
and provides low-cost simple fusion schemes. Interest in
research on MIF has recently been stimulated by:
1) laser-drive magnetic flux compression experiments,
2) the approach to a high β magnetic systems, and
3) advantages in plasma guns and lasers.
Inertially confined plasmas have the attraction that
equilibrium, MHD stability, and microinstability prob-
lems associated with magnetic confinement can be
avoided. The possibility of efficient laser heating of
significantly lower plasma densities confined in mag-
netic configurations appears very remote. The advan-
tage of such a hybrid scheme is that the output of any
individual laser may be reduced.
At the density near 1023 m-3 steady state magnetic
confinement at thermonuclear temperatures is possible.
Such an approach is to heat a linear high β device. An-
other possibility is laser heating of magnetically con-
fined plasma.
In this paper spherical configuration of magnetic
field for laser driven MIF is proposed. Ultrahigh inten-
sity magnetic filed that can be generated by laser-driven
magnetic flux compression of the spherical configura-
tion (e.g. cusp or compact toroid) are made. Power bal-
ance of high density and temperature plasma in ultra-
high magnetic fields is analyzed.
Critical to the success of such experiments is to per-
form full-up multidimensional computational simula-
tions of them [29]. However, there are numerous diffi-
culties in performing those simulations.
Part of this work was supported by Grant No. RFBR
No 09-08-00137.
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Статья поступила в редакцию 02.06.2010 г.
О ПОВЕДЕНИИ ЗАМАГНИЧЕННОЙ ПЛАЗМЫ ПРИ ВОЗДЕЙСТВИИ НА НЕЕ ЛАЗЕРОМ
С ВЫСОКОЙ ЭНЕРГИЕЙ ИМПУЛЬСА
С.В. Рыжков
Рассмотрен магнитно-инерциальный термоядерный синтез с лазерным драйвером. Представлено моде-
лирование сильно нелинейного режима взаимодействия мощного лазерного импульса с предварительно за-
магниченной плазмой. В качестве мишеней выбраны магнитные системы удержания плазмы антипробко-
трон (касп) и компактный тор (обращенная магнитная конфигурация). Обсуждаются вопросы самосогласо-
ванного и внешнего приложенного магнитного поля. Проведен анализ энергетического баланса D-T-плазмы
при сферически симметричной имплозии мишени лазером с высокой энергией импульса. Получены основ-
ные энергетические характеристики плазменной мишени, вмороженной в магнитное поле.
ПРО ПОВЕДІНКУ ЗАМАГНІЧЕННОЇ ПЛАЗМИ ПРИ ДІЇ НА НЕЇ ЛАЗЕРОМ З ВИСОКОЮ
ЕНЕРГІЄЮ ІМПУЛЬСУ
С.В. Рижков
Розглянуто магнітно-інерціальний термоядерний синтез з лазерним драйвером. Представлено моделю-
вання сильно нелінійного режиму взаємодії потужного лазерного імпульсу з попередньо замагніченною пла-
змою. В якості мішеней вибрано магнітні системи утримання плазми антіпробкотрон (асп) і компактний тор
(звернена магнітна конфігурація). Обговорюються питання самоузгодженого і зовнішнього прикладеного
магнітного поля. Проведено аналіз енергетичного балансу D-T-плазми при сферично симетричній імплозії
мішені лазером з високою енергією імпульсу. Отримано основні енергетичні характеристики плазмової мі-
шені, вмороженої в магнітне поле.
О ПОВЕДЕНИИ ЗАМАГНИЧЕННОЙ ПЛАЗМЫ ПРИ ВОЗДЕЙСТВИИ НА НЕЕ ЛАЗЕРОМ С ВЫСОКОЙ ЭНЕРГИЕЙ ИМПУЛЬСА
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