J. Plasma Fusion Res. SERIES, Vol. 8 (2009)

Alternative Fusion Reactors as Future Commercial Power Plants
Sergei V. RYZHKOVBauman Moscow State Technical University(Received: 29 August 2008 / Accepted: 1 April 2009)

Alternative reactor based on a field-reversed configuration (FRC) has advantages of the cylindrical geometry,the open field line geometry (direct energy conversion (DEC) of the charged-particle flow), and high � (plasmapressure/magnetic-field pressure). This paper aims to evaluate the attractiveness of a low radioactive FRC fusion
core. Analysis of a conceptual deuterium - helium-3 (D-3He) fusion power reactor is presented and reference point
is defined. Principal parameters of the D-3He plasma reference case (RC) and comparison with conceptual D-3He
tokamak and FRC power plants are shown.
Keywords: advanced fuel, alternative concept, aneutronic reactions, bremsstrahlung, compact toroid, field reversed
configuration, low radioactive reactor, magnetic confinement.

The main advantage of RMF is that as plasma
shaping or ion beams RMF would be needed for stability.
Various plasma parameters are given in [5] for RMFformed plasmas and theta-pinch formed plasmas.
Appropriate hot, steady-state FRCs can now be formed
using RMF and scaling laws developed for achievable
RMF sustained FRC flux levels [6].
Current drive rotating magnetic fields has been
extensively explored in a series of spherical rotamak(oblate FRC) experiments at Flinders University inAustralia [7]. The most extensive development of RMF
current drive in more standard prolate FRCs, inside a flux
conserver, has been carried out in the TCSU experimentat the University of Washington [8].
The possibility of using the whole energy of thefusion reaction directly thru the DEC system is very
attractive. A FRC burning low radioactive fuel has: lesscomplexity - simple cylindrical geometry, low activation- relative easy maintenance, and effective ash removal natural divertor. This paper aims to evaluate theattractiveness of a steady state D-3He FRC fusion power
plant as future commercial reactor based on RMF current
drive for startup and sustainment.
The aneutronic reactions used in the analysis ofadvanced fuels and alternative schemes are very sensitiveto nuclear reaction cross sections and fusion reaction rate.
Improved formulas for fusion cross-sections and thermal
reactivities may be found in [9-12].
From the point of view of the radioactivity effects
the fusion reactions can be separated in two categories,
according to the case where they include radioactive
elements in the reacting fuel (tritium) and in the reaction
products (neutron and tritium). Category one(radioactivity production):

1. Introduction

The FRC [1,2] is a confinement device (FRC plasma
is a toroid with the exclusively poloidal magnetic field)
combining of properties and prospects of the open andclosed magnetic system and leading to very large reactor
advantages (see Fig. 1). Actually, FRC experiment wasstarted in Russia (TRINITI) and USA (LANL) in 1970s.
Review papers have been published in the 1980s [3,4].
Stages of FRC formation include: 1) preionization; 2)field reversal; 3) radial compression and field lineconnection; 4) axial contraction; and 5) equilibrium.
Since FRCs have traditionally been formed intheta-pinches, they are generally shown horizontal incontrast with the depiction of other toroidal plasmas. TheFRC acts as an excluded flux object or an infinitelyconducting object bounded by it separatrix.
The FRC plasma can even be formed by merging
spheromaks of nearly opposite helicities, indicating ahigh state of self-organization.
The rotating magnetic field (RMF) power
current-drive is the power required to replaced themagnetic energy dissipation caused by resistive friction.
In contrast to theta-pinch RMF provides confinement.

Fig.1

Magnetic flux in the elongated FRC. Closed fieldlines are inside the separatrix (green), open field lines are purely
poloidal field (violet). The direction of azimuthal current isshown by crosses.
author’s e-mail: ryzhkov@power.bmstu.ru

35©2009 by The Japan Society of Plasma
Science and Nuclear Fusion Research

S.V. Ryzhkov, Alternative Fusion Reactors as Future Commercial Power Plants

T ( d , n ) 4 He + 17589 keV(1)

3

D ( d , p ) T + 4033 keV

(2)
(3)

T ( T , 2n ) 4 He + 11332 keV(4)

D ( d , n ) He + 3269 keV

Category two (little or no radioactivity production):
3
6

He ( d , p ) 4 He + 18353 keV
3(6)Li ( p , He ) He + 4018 keV

113(5)444

B ( p , 2 He ) He + 8681 keV(7)He ( 3 He , 2p ) 4 He + 12860 keV(8)Reaction (5) is not fully aneutronic due to the D-D
reactions, but deuterium – helium-3 reaction has thehighest known specific fusion power. Positive power
output for the ignition and sustainment (plasma gain or
amplification factor ~ 10) of a D-3He plasma may bereached at 40-90 keV [13-15]. Reaction (8) has no direct
and indirect radioactivity at all.
Section 2 describes the FRC plasma. A referencecase is exhibited, and comparison of D-3He tokamak andFRC reactors are discussed in Sec. 3.

2. FRC Fusion Core

Typical pictures of the magnetic flux function,
calculated according to Steinhauer analytical equilibrium
model (SAE) [16], are shown in Fig. 2. Upper one isrelevant to FRC conceptual projects and presents
elongated Hill's vortex [17] with elongation

Fig.2

BB

The physics and models used in the present analysis
are described in details in papers [1,2]. So, only improved
Bauman formulas [20] for the total bremsstrahlung losses(power in MW/m3) including radiation on both ions andelectrons are presented here:E � ls / rs � 5 � 15 . Racetrack is shown below withE � 3 � 5 that is characteristic for experimental
parameters. Parameters used for the calculation are
averaged for the experiments and reactors.
Note that paper [16] has type errors. The right
expression for the shape index is [18]:N � b 2 / aRs �2�4�E1 � 3��5 E22� ��E1 � �� (2 � � ) E2 ���Contour plot of the flux magnetic function for a prolate
field reversed configuration: 1) elongated Hill's vortex,
B0 = 10 T, ls = 8 m, rs = 1 m, and 2) racetrackequilibrium, B0 = 1 T, ls = 0,4 m, rs = 0,1 m.

Pei � 1.7 �10�35 ne2 y1/ 2 Z eff � Log (2 y � 0.5)
� 0.928� � exp(�2 y ),(10)Pee � 2.57 �10�35 ne2 y 3 / 2 �1 � 1.17 y � 0.28 y 2 � 0.6 y 3 � , 11)��where ne is the electron density, Z eff is the effective
charge,Te is the electrony � 103 Te e /(me c 2 ),temperature in keV, e is the electron charge, me is theelectron mass, and c is the speed of light.
The main radiation loss channel in hot FRC D-3He
plasmas is bremsstrahlung, which gets over 20% of thetotal fusion power. Bremsstrahlung loss is soft x-ray
radiation that cannot be converted directly to electricity
as can charged power particle or, possibly, synchrotron
radiation. The correct bremsstrahlung radiation power isshown in Fig. 3. Comparison made with [21-23].

,1/ 2where � � 1/ �1 � (� / �) 2 � .
��It is difficult to find exact Grad-Shafranov solutions
to match the cylindrical flux excluding boundary for an
FRC. It is especially difficult to find solutions for an
elongated FRC or one with more racetrack like separatrix
than the elliptical type profile. Models [17,19] haveelongated configuration (ellipsoid) and do not have ananalytic external solution. But experiments haveelongated shape like racetrack. SAE satisfies bothexperiments and reactor regimes and is a more generalequilibrium with external and internal solutions.

36

S.V. Ryzhkov, Alternative Fusion Reactors as Future Commercial Power Plants

8The ratio S*/k has been used to delineate FRC
stability regimes, where k = Ls/rs is the plasma
elongation, and S* is defined by��

�

��

6�

���

�

�

4�

�

�
�

2��
�

0 ���
0Fig.3�����

Svensson�Bauman�

McNally�

Rider�
��
�

�
�
�

�

�

�

�

�

50100

��

�
�

�

�

150S * � rs � pi / c � 0.3 rs / �i ,(12)where Ls is the separatrix length, �pi is the ion plasma
frequency, �i is the ion gyroradius, and c/�pi iscomparable to the ion gyroradius for � � 1.
Although definitive limits on S* / k or S*/ E have notyet been established, the condition of gross stability forpresent experiments leads to the condition S*/ E � 3.5.
Anticipating improvement and because the large
fusion-product gyroradii will contribute to FLR
stabilization, S*/k � 3.5 is used for the reactor study, forthis paper's reference case. Figure 4 shows FRC operating
regimes [24] for some experimental devices and designprojects.

200

Bremsstrahlung power per unit volume plotted versus
electron temperature. Calculations made for the electron
density ne=5 1020 m-3 and the impurity coefficient
Zimp=1.75. The Bauman fit described in the text isshown as boxes.

Bremsstrahlung may be estimated with good
accuracy by these formulas. Bauman fit is more precise
for the temperature range 10-100 keV that is crucial for
aneutronic fusion.
The impact on reactor application is significant.
Difference in bremsstrahlung losses just 3% essentiallychanges power balance and leads to decreasing of fusion
amplification factor. So, correct calculation ofbremsstrahlung is very important, especially for low
radioactive fuel.
Fig.4

3. Reactor Study

Operating regimes for experimental FRCs and D-3He
FRC conceptual power plants.

Table 1 Comparison of the main parameters for D-3He tokamak (T) and FRC power plants (reactor study).
Parameter
Electrical power
Fusion power
Bremsstrahlung
Synchrotron radiation power
Transport power
Neutron power
Injected (current drive) power
Net efficiency
Neutron wall load3
He to D density ratioPlasma major(separatrix) radius
Minor radius (separatrix length)
Ion temperature
Electron temperature
Electron density
Ion density
Plasma current (I/k)
TF on axis (external B-field)
Averaged beta
Energy confinement timeApollo (T)1000 MW2144 MW652 MW
1027 MW456 MW
147 MW(138 MW)
0.43
5.7 MW/m2
0.63
7.89 m2.5 m
57 keV51 keV
1.9 x 1020 m-3
1.3 x 1020 m-3
53 MA
10.9 (19.3) T
6.7 %
16 s

ARIES-III (T)1000 MW2682 MW
Radiation fraction
0.72
110 MW(172 MW)
Recirc. power 0.24Aver. 0.08 MW/m2
~1
7.5 m
2.5 m
55 keV
53 keV
3.3 x 1020 m-3
2.1 x 1020 m-3
30 MA
7.6 T
Toroidal 24 %11.8 s, �p/ �E = 237

Artemis (FRC)
1000 MW
1610 MW
Total radiation
357 MW
1181 MW
77 MW
5 MW
0.36-0.62
0.27 MW/m2
0.51.12 m17 m
87.5 keV
87.5 keV
6.6 x 1020 m-3160 (21) MA(6.7) T90 %2.1 s

D-3He FRC (RC)1000 MW1962 MW776 MW
8.7 MW
1188 MW
51.7 MW
62.6 MW
0.49
0.15 MW/m2
11.23 m30.75 m68.5 keV68.5 keV
5.4 x 1020 m-3
3.46 x 1020 m-3
298.8 (24) MA(6.38) T
74.8 %
1.44 sS.V. Ryzhkov, Alternative Fusion Reactors as Future Commercial Power Plants

Reference case (RC) is presented in Table I. Fourmain D-3He conceptual designs are shown: Apollo [25]and ARIES-III [26] are D-3He fueled tokamaks, Artemis[27] together with the last one proposed by the author areD-3He FRC reactors.
We see in Table I substantial advantages of D-3He
FRC power reactors: higher charged particle transportpower and �, lower injected power and magnetic field.
The advantages of D-3He tokamaks: lower temperatureand higher energy confinement time.
The reference case possesses a high plasma current,
but it is important to recognize that this current stretches
axially along the device and has a short poloidal path. For
this reason, the current/elongation I/k is a better index of
the difficulty in creating and maintaining the current. For
this design I/k=24 MA. The analogous value in, forexample, a D-3He spherical tokamak power plant, is I ~70
MA, in that case for fusion power 1400 MW.
The recent Artemis conceptual D-3He FRC power
plant design differs from these assumptions by invoking
field-reversed theta-pinch FRC formation, translationfrom the formation chamber to a burn chamber where
neutrals beams sustain the plasma, and traveling wave
direct conversion of the ~15 MeV D-3He fusion-productprotons before they slow down on the background plasma(energy confinement time � E � 0 ).
Because of small neutron wall load the power plant
wastes will be have low radiatioactivity. FRC using
advanced fuel has the following best parameters: lower
neutron wall load ~ 0.2 MW/m2 and higher fusion power
density ~ 15 MW/m3.
The optimum size of a reactor based on CT has rs
little larger than thickness of the blanket, shield and coilwhere rs is the smallest characteristic size. Comparison
with a conceptual D-3He tokamak power plant designindicates that a D-3He FRC reactor would be even more
attractive.
In addition, a few projects investigated advanced
fuel cycles (with D-D and D-3He) and non-electric
applications of fusion along with technological means tolessen the likelihood of proliferation [28-33].
I am indebted to John Santarius for his interest andadvice in this research.

S.V. Ryzhkov et al., Fusion Science and Technology 43(1T), 304 (2003).
[3] M. Tuszewski, Nucl. Fusion 28, � 11, 2033 (1988).
[4] R.Kh. Kurtmullaev et al., in book Results of science andtechnique. Plasma Physics Ser. 7, edited by V.D.
Shafranov (VINITI, Moscow, in Russian), 80 (1985).
[5] A.L. Hoffman, FRCs Course AA559, University ofWashington (2007). hoffman@aa.washington.edu.
[6] A.L. Hoffman et al., 22nd IAEA Fusion EnergyConference(Geneva,2008).
See
http://www.fec2008.ch/preprints/ic_p4-1.pdf.
[7] I. Jones, Phys. Plasmas 6, � 5, 1950 (1999).
[8] A.L. Hoffman et al., Fusion Science and Technology 41,92 (2002).
[9] H.-S. Bosch, and G.M. Hale, Nuclear Fusion 32, � 4,611 (1992); Nuclear Fusion 33, �12, 1919 (1993).
[10] W.M. Nevins, and R. Swain, Nuclear Fusion 40, � 4,865 (2000).
[11] R. Feldbacher, Nuclear reaction cross sections andreactivity parameter library and files (Vienna: IAEA,1987).
[12] FENDL, http://www-nds.iaea.org/fendl/fen-fusion.htm.
[13] G.H. Miley, Nuclear Instruments and Methods 207, 111(1983).
[14] W. Kernbichler, Fusion Technol. 21, 2297 (1992).
[15] S.V. Ryzhkov et al., Fusion Technol. 39, 410 (2001).
[16] L.C. Steinhauer, Phys. Fluids B 2, � 12, 3081 (1990).
[17] M.J. Hill, Philos. Trans. R. Soc. Ser. A., Pt.1, C/XXXV,
213 (1894).
[18] Loren Steinhauer, private communication.
[19] L.S. Solov’ev, in Reviews of Plasma Physics 6, edited byM. Leontovich (Consultants Bureau, New York), 239(1976).
[20] A.Yu. Chirkov et al., Fusion Science and Technology 39(1T), 402 (2001); V.I. Khvesyuk et al., in Proc. of IIRussian National Conf. on Heat Exchange 6 (MPEI,Moscow, in Russian), 382 (1998).
[21] R. Svensson, Astrophys. J. 258, 335 (1982).
[22] J.R. McNally, Nuclear Technology/Fusion 2, 9 (1982).
[23] T.H. Rider, Phys. Plasmas 2, � 6, 1853 (1995).
[24] R.E. Siemon et al., ITC-12 (Toki, 2001).
[25] G.L. Kulcinski et al., Fusion Technol. 21, 2292 (1992).
[26] F. Najmabadi et al., Report UCLA-PPG-1384. 1994
http://aries.ucsd.edu/LIB/REPORT/ARIES-3/final.shtml.
[27] H. Momota et al., Fusion Technol. 21, 2307 (1992).
[28] B. Coppi et al., Fusion Technol., 25, 353 (1994).
[29] M.V. Krivosheev, and V.N. Litunovsky, Fusion Technol.
27 (1T), 337 (1995).
[30] N. Rostoker et al., Science 278, 1419 (1997).
[31] M.J. Schaffer et al., US-Japan Workshop on Physics ofCompact Toroid Plasmas (Seattle, 2002). See
http://www.aa.washington.edu/AERP/RPPL/us-japan-feb2002/schaffer.pdf.
[32] S.A. Cohen et al., Phys Plasmas 14, 072508 (2007).
[33] J.F. Santarius, G.L. Kulcinski, L.A. El-Guebaly, Fusion
Science and Technol. 44, 289 (2003).
[2]

This work was supported by the Federal Agency for
Science and Innovations Rosnauka (Grant of thePresident of the Russian Federation � MK-676.2008.8)
and Russian Foundation for Basic Research (RFBR
Grants � 09-08-00137-� and � 08-08-09244-mob_z).

References[1]J.F. Santarius et al., Report UWFDM-1129 (2000). See
http://fti.neep.wisc.edu/pdf/fdm1129.pdf.

38