Abstract : An explanation of the present ideas about the design of a home-made ultra small torus is given. The size of the device is restricted to the available funds as usual . At the moment only a rough idea of the dimensions, type of the device and other parameters is known. The objective is to experiment with the technologies used in fusion experiments. In any case the very small size of the device does not allow any plasma research.

Ideas that are analysed: 

   Alternative concepts.  

   Small tokamaks : 

       Energy confinement time. Line radiation. Power supplies. Plasma current. Length of pulses.

   Small stellarators:

       Types of stellarator. Superconductor coils - resistive coils. Classical stellarator - torsatron.

Approaches and rough calculations
 

   Decision one, 1) :  What type of device should be built? .

   a) Torus (tokamak or stellarator) or

   b) Alternative concepts (spheromak, FRC, RPF, dipole, Electostatic-IEC, colliding beams, other inertial methods ...)

   Due to my limited knowledge about the alternative approaches and the future likely less applicability of the obtained knowledge from alternative devices, the alternative a) is taken.

   2) Tokamak or stellarator? Result : stellarator. The next are the reasons.

Some months ago the idea of a tokamak seemed  attractive and some calculations were carried out. The main features and difficulties to build an ultra low cost device are explained below.

Previous ideas about very small tokamaks

    ETE (Brazilian tokamak) and ITER were taken as examples to compare the estimations of parameters. ETE was considered because it is a very simple tokamak. ITER because it is well documented.

   * One important problem is the very low energy confinement time (order of 10^-5 s, calculated as H-mode, so consider 1/2 for L-mode) for a device about 6 times smaller than ETE. This low confinement time imposes other no satisfactory conditions to the design that we will discuss later.

   * Another issue is the low plasma temperature taken into consideration, from 20eV to 100eV, that results in a working point that has high line radiation even for low Z elements.

   Line radiation : For T=50eV ; concentration of the high radiation elements at this T  = 0.001 ; element considered = Nitrogen . Line radiation results 8 x 10⁴ J/m³. Because the device is very small it results only 126W

But a more realistic concentration of N , O, H2O ... in a home-made device could be 1% and the radiated power then is 1.3kW ,  still a reasonable value.

Energy confinement time

   For T=50eV , loss of energy is about 10MW/m³ that results 3 x 10⁴ W  for the device. This density of power is even higher than in ETE. A very short, high power pulse is necessary to heat this very bad isolated plasma (due to the small size of the device) .

   Taking Bt = B toroidal = 0.2 T due to toroidal coil and power supplies limitations, it gives about max Ip=4000 A  from very basic stability considerations.

   For Ip=4600A , T=50eV and the condition of thermal equilibrium (line radiation + energy losses + Bremsstrahlung losses ~ 0 = Ohmic heating) results Uloop = voltage loop = 3V . This has been calculated from an approximate expression of the plasma resistance that gives also a good order of magnitude for ITER.

It is difficult to reach Uloop = 3V using an OH coil in a compact tokamak. The original design was geometrically similar to ETE so the OH coil is slender and has a small transversal section, resulting even in less performance. For a slender OH coil the power dissipated by joule effect were higher than 10MW. The pulse lasts 0.002 s . 

For an OH geometry similar to HT-7U and ITER the joule power is still higher than 1MW. OH Voltage is about 6kV .  Currents are of the order of +-5000 A.

No combination of values gave a reasonable solution. The required power is even higher than in ETE. This seems an indirect consequence of the low energy confinement time when the size is reduced.

 The difficulties of this design are : A low performance bank of condensers cannot achieve this values, tensions involved are too high, forces in the OH coil will be extremely high, the pulse must be too short to be easily analysed, even with a short pulse the temperature reached in the coil (adiabatic calculation) is notable.

    The idea of this small tokamak was abandoned.

Recent ideas about a very small stellarator

   Due to the no necessity of plasma current to maintain the plasma confinement, a plasma at very low T can be imagined. This idea could result in no more than a kind of light bulb but at least is a beginning.

    CTH torsatron at Auburn University is the main stellarator used here as a model. This is a notable simple and small stellarator with resistive coils. As a first try a 10 times reduction of scale has been roughly calculated.

   Other types of stellarators, like the modular helias W7-X,  LHC torsatron, heliac TJ-II , the compact stellarator-tokamak NSCX has taken into consideration to try to obtain ideas for the design.

  Superconductor coils or resistive coils?  The decision is resistive coils at least as a first experience. The reasons are the next:

HTS superconductor coils seemed a good idea. LTS conductors is nearly impossible. Working at 77K or better at 65-70K using subcooled LN2 , Bi2223 HTS superconductor gives a low but useful performance. YBCO is not commercially available.

   Superconductor difficulties. The first issue is to obtain the superconductor. At this moment there are no available suppliers for small orders. The standard 1mm² Bi-2223 wire allows a max theoretical current of ~100A. The result is satisfactory considering a coil with a high number of turns and low current.

   Roughly 10 litres of LN2 are necessary to cool down the coil considering a slow cooldown.

   However the best and economical cooling system is not clear. A kind of CIC conductor with one (or several) wires inside a plastic jacket is not easy for a home-made conductor. An aluminium or steel jacket is nearly impossible.  The use of a boiling pool is the simplest method but the channels to cool the wire diminish the strength and accuracy of the winding pack. The use of an adiabatic construction is highly unestable and tend to quench.

   To reduce the cost of the power supplies the wire must be long and the number of turns high. As a result the CIC option is less convenient because of the high number of parallel cooling channels to assemble to suit the LN2 pumping conditions.

     The boiling pool is the best option under the last conditions. The cooling channels should be design in a simple and creative way. The pool might be the case of the winding, opened in all the upper section. 

   The decision is to build a small superconductor magnet, develop the cooling and control systems and abandon the idea of a superconductor helical coil.

   Classical stellarator or torsatron?

   On the one hand the torsatron has the disadvantage of the existence of poloidal coils and the powers supplies to feed these poloidal coils in order to adjust a cero stray field (otherwise the coils should be perfect). On the other hand the forces between windings are lower  than in a classical stellarator. Vacuum magnetic surfaces might be more adecuate in torsatrons, but it is not clear at the moment if a classical stellarator can generate the same magnetic fields than a torsatron. In any case the forces involved in the device are low due to the small value of the magnetic fields.  As a consecuence the election of a classical stellarator might be simpler since no PF coils are necessary. However the coils of the classical stellarator are slightly more complex than in a torsatron.

  Further developments
 

   A further comparative study of the engineering characteristics of torsatrons and classical stellarators is necessary to decide what alternative suits better the requirements of low cost, simplicity, utility to learn and for future applications of the acquired knowledge.

Last Update 30-06-2005