Comparison of innovative concepts to help in the decision of the UST_2  fusion experiment.  Dipole and FRC (Part 1)    



Abstract :  Basic features are analysed for several fusion concepts, particularly the ones that have implications in the engineering cost and difficulty. Stellarators and tokamaks excluded. Cost of coils and maintenance, Beta,  possibility of advanced fuels, current drive, energy confinement times, particle handling and reactor studies are analysed. The study is divided in 3 Parts, two devices per page. The comparison of the basic features and recent experimental results should help in the decision of a new fusion device, UST_2. If there is not a device  more convincing than a stellarator, UST_2 may be a stellarator.



* Dipole and FRC   (Devices analysed in Part 1 )


See Part 2 and 3 for :

RFP, Spheromak

Spherical tokamak, IEC

 Stellarator and tokamak not studied here.



   One and a half years ago the analysis of different devices was omitted due to lack of knowledge [100].  The objective is to clarify the alternatives to design a small device for fusion research in engineering. In [100] the result was to build UST_1 stellarator which finally was designed and built as an optimised modular stellarator with external resistive coils on a circular toroid, plaster frame for grooves and copper vacuum vessel. UST_1 has obtained good magnetic surfaces and some initial plasmas.


   Important additional knowledge has been acquired from then, many spreadsheets are of immediate use, a flexible and powerful JAVA code has been developed to simulate, calculate and optimise configurations of coils, many creative and risky techniques, successful and unsuccessful, have been experimented. Building a new stellarator similar to UST_1 would be a matter of one or two intensive months of work and about 300€ of cost. However such a possibility lacks of sense.  


   Some new key engineering features should be included in the new design. Additionally the physics design should be improved, however it might depend on the help of experts in plasma physics.


   UST_2 does not need to be a stellarator. Any other fusion device with better perspectives as a reactor could be chosen.


   In principle  UST_2 is not intended to be constructed without some funding and/or interest from foundations, university, company, sponsor, etc.


  The next compilation will be expanded in the future if new or more accurate information is found. 

  Maybe a table will be completed when all the devices had the same basic data. It will help to have a global vision.






   No-one can be an expert in all fusion devices so some inaccuracies surely will appear in the next comparisons of devices. If you know about one of the devices as a fusion reactor and would like to correct some mistakes, add recent data or an opinion, please send further experimental data supported by reasons. Scaling laws, based even in very reduced experimental results only to have an order of magnitud, are extremely important in concepts barely studied.







   References [10] to [19] plus general ones (in dipole not assigned at each particular information)


   LDX, CTX, mini-RT , RT-1  devices. Unluckily  experimental data for dipoles is very incomplete. The superconductor levitating central ring is the main issue (refrigeration and levitation).


Advantages : Simple, easy access for maintenance,  economical (if the central ring is feasible). Excellent confinement and the posibility of a D-T burning plasma device of reduced size, however not possible CW with D-T. Low magnetic field inside the plasma (high Beta) so low cyclotron radiation ~ suited for advanced fuels. Free of disruptions. No current drive.


Levitating ring : Levitation seems achievable even with weighty rings for reactors. 24% of the neutrons (excesive using D-T) and photons will reach the floating coil. The convectional flow (related to Tau E) remains unknown and it is so difficult to dissipate as neutronics and radiation (supposing 3He and specular surfaces). The radiation of more power than received by the floating ring should be studied carefully.


Stability : LDX : Fuelling seems necessary to maintain stability. High neutral pressure seems necessary for stability (2-4e-6 Torr)  but larger plasmas seem less demanding.


Alpha heating regime : Collective alpha-driven instabilities and alpha transport is not clear [1].


Energy confinement time and transport: LDX : From 50 to 100-200 depending on the 2.45GHz power fraction.  5 ms post-RF. Convective cells increase transport but quantitative values are unknown. "Reaction products may affect pressure distribution, driving strong convection" [1].
Turbulent transport is not clear. Theory supports that turbulent transport is not relevant.


Beta : Beta peak of 20% (LDX) , 35% , 8% and 8% (Dolan) are achieved in different devices. Sharp profiles. Beta > 1 are theoretically possible.


Advanced fuels : Perhaps helium catalyzed D-D (D-3He self-produced) or D-3He . Convective cells phenomenon could be useful to remove T before an important fraction of it burns. Risk of T  acumulation. It is acceptable if excessive cost of 3He from the moon or other planets.


Self-heated and CW/pulsed :  Self-heated , CW


Current drive  : NO


Particle handling :  No problem with outwards flux. Critical the heating of the ring, almost impossible to withstand.


Example of reactor : Fusion power 600MW for 60m diameter and 30m height. Power concentred near the central ring with extreme gradients near the ring. The size of a reactor is slightly large (it is for 3He but D-T seems impossible).


Critical issues :  Ring heating-cooling~ 3He possibility ~ Beta limit+Tau E.









Field Reversed Configuration



References [20] to [29] plus general ones. 


The  experimental data for FRC is still very incomplete.


Devices : [20] : TCS at UW , Swarthmore Spheromak Experiment (SSX-FRC) at Swarthmore College , Rotamak experiment at Prairie View A&M University, Ion ring FRC experiment at Cornell University,  Antiparity RMF experiment at PPPL.  TS-3/4 at University of Tokyo, FIX at Osaka University, NUCTE III Translation Experiment at Nihon University deevices.



Advantages : Simple, linear geometry, low magnetic fields (~economical coils), open divertor, easy access for maintenance, small size, perhaps economical. D-T burning plasma device of reduced size. Low magnetic field inside the plasma (high Beta) so low cylotron radiation ~ suited for advanced fuels.  Free of disruptions [1]. Able for direct conversion of energetic particles with 3He fuel. Relatively simple maintenance of the blanket.



Stability : Stability at R/rhoi=4 [3], evidence of self-organization, Rotational stabilization. Strong kinetic stabilization. Global motion (n=1) is an issue (FIX), stabilized   by NBI [20]. Internal tilt and rotational need to be addressed.


Alpha heating regime : Collective alpha-driven effects at Bt = 0 will affect instabilities [1] . Certain alpha effects may be stabilizing [1] . The influence of alphas is not clear.


Energy confinement time or flux lifetime and transport :

Pulsed, empirical : τphi proportional to  rs2 √n [20]

Flux lifetime = flux confinement time = about 50% superior to 9√xs (rs[m]/√ρi[cm])2.14 . rs = edge plasma radius (proportional to  Te1.32 ) and from 0,1 to 0.15ms in TCS [20]

Te ~ 40eV in FIX using ~200kW NBI [20]

Tt =  Te + Ti = 40eV in TCS (Te~20eV) under RMF 2.5ms [20], ne = 1e19 m-3 Be = external field =~10mT.

Tt = 50eV  TCS  [23]

There is a scaling law for ne = f(Bw , w ,  rs) [20]

Temperatures limited by high impurity contact due to unbaked, non conditioned  vacuum chamber [20].

Rotamak : 40ms FRC by RMF

B = magnetic field =~10mT [23]

Theoretically strong plasma turbulence develops when vde exceeds vs [23]



Beta :  Very high Beta  . 

β = 1 – xs 2/2  (in RMF mode)   xs  =  plasma radius / coil radius (perhaps no very high in D-T, due to shield. Beta ave. theoretical > 65% [23]

Experimental Beta : Not known.


Advanced fuels : 3He , From 2 to 4% of power from neutrons (relation 1:1 and 3:1 at 50keV) [24] . Perhaps possible due to high Beta (low B, low cyclotron radiation) and low fields.



Self-heated and CW/ pulsed :  Self-heated , CW or pulsed.

One FRC plasma in TCS lasted 0.2ms [20]. RMF plasma in TCS lasted ~ 1.4ms [23]


Current drive  : YES.  Perhaps rotating magnetic fields (RMF) (U. Washinton) [4] (~Rotamak) and NBI. TCS , 60kA of RMF current drive during 2.5ms (power supply limited [23])

Possible current drive by selective loss of alphas [1]


Particle handling : Easy maintenance and construction of and open axial divertor. Neutron loads remain in D-T mode.


Maintenance : Simpler than in tokanaks. Easy replacement of divertor.


Example of reactor : 'ARTEMIS' [21] . ne ~1e20 m-3 (achieved 3e19 m-3),  s > 25 (achieved 4 in LSX). nm =  1e20m-3 , Tt= 25KeV , Be = 1T , Rs=2.5m , fw =10kHz, fr=4.7kHz, vde =1.5e5m/s  ,  vs = 13e5m/s , vde/vs~0.13 [21] (achieved 4 in present exp.) [23]


Critical issues :   - Reliable and low cost sustaintment of flux. 






 Reasons and insights to chose a suitable

device for UST_2


     A decision will be taken some time after the end of the study of the devices.








[1] "Comments on Innovative Confinement Concepts
and Burning Plasma Science" E. B. Hooper

[2] "Fusion research : Experiments " T. J. Dolan , Pergamon Press.

[3] "Fusion Energy Science Opportunities in Emerging Concepts" Los Alamos National Laboratory Report -- LA-UR-99-5052


[5] "MFE Concept Integration and Performance Measures" Magnetic Fusion Concept Working Group ,  M.C. Zarnstorff, D. Gates, E.B. Hooper, et al.



[10] "Helium Catalyzed D-D Fusion in a Levitated Dipole"
J. Kesner, D.T. Garnier†, A. Hansen†,

[11] "Controlling Interchange Instabilities in the Levitated Dipole Experiment"  Darren Garnier and the LDX Team. 

[12] "Abstract : An important topic being investigated in the Levitated Dipole Experiment (LDX) is the effect on confinement ..."  Web

[13] "Helium Catalyzed D-D Fusion in a Levitated Dipole" J. Kesner, D.T. Garnier†, A. Hansen†, M. Mauel†, L. Bromberg, Plasma Science and Fusion Center, MIT.

[14] "The Dipole Fusion Confinement Concept:
A White Paper for the Fusion Community" J. Kesner and L. Bromberg



[20] "Recent Progress on Field Reversed Configurations
(FRC)" Houyang Guo

[21] "Conceptual design of D-3He FRC fusion reactor 'ARTEMIS'  " H. Momota, A. Ishida,  G. H. Miley at al. 1991, NIFS-101

[22] "FRC power plants - A fusion Development Perpective". J. F. Santarius, G.A. Emmert, G. H. Miley et al. , 1998

[23] "Confinement & Current Drive Measurements for Steady-State FRCs" Alan Hoffma, Innovative Confinement Concepts Workshop

[24] D-3He Physics and Fusion Energy prospects"  J. F. Santarius and L. Kulcinsky. FTI  ,  U. of Wisconsin . Innovative Confinement Concepts Workshop, Madison Wisconsin , 2004



[100] "First approaches for the design and construction of an ultra small torus to experiment with fusion technologies" Vicente M. Queral. See "List of all R&D"












Date of publication 26-02-2007. Continuous addition of data