Energy confinement time and estimation of the heating system in UST_1    



Abstract : The energy confinement time for UST_1 and for other real experiments is calculated. The heating system is outlined.


                       Energy confinement time

    Two expressions are used to calculate the energy confinement time (TauE) in UST_1 under several conditions, ISS04v1 and ISS95 obtained from [1].

   The expressions are tested against the experimental TauE in other small or medium stellarators. The small ones are the most interesting here.

   Conditions of the calculation : About 50% of the available heating power is transmited to the plasma. The geometrical size is the standard if no other is mentioned in each particular experiment. Density, temperature of ions and electrons (average if different) and Iota mostly come from the experiment data. The enhancement factor (a) in TJ-II and W-AS come from [1]; the others are calculated factors to approximate the experimental result. (d) is the energy confinement time for the particular experiment. ISS95 is scaled with the same enhancement factor applied to ISS04v1 as a means of comparison.

   Line radiation is calculated from : table Chapter 3F in Dolan, one expression from [12] and another expression. Big discrepancies are observed in the results but any value is negligible even for 10% of O2 impurity (similar for N2). The table in Dolan is supposed to be the accurate calculation.



Name (a) Enh (b) ISS04 (c) ISS95 (d) Exper.
  ms ms  
CTH 1 1,320 0,970 x
TU-heli 0,2 0,061 0,049 0,070
W 7-AS 1 17,900 10,600 50,000
WEGA 0,5 0,186 0,168 0,050
TJ-II 0,25 4,140 2,030 4,000

  Origin of the data for the above calculation :

CTH from [2] , TU-Heliac [3] and [4] , W 7-AS [5] and others , WEGA [6] and [7] , TJ-II [8]


* In general the approximation is notable, as it should be. However the enhancement factors cannot be calculated and [1] give data only for a few present stellarators.

* In WEGA the result is quite different, the experimental result can be obtained with an enhancement factor of 0.13 . However [6] states a theoretical TauE =150ms .

* In TU-Heliac the enhancement factor Enh= 0.2 is obtained to adjust to the experimental value.

* In TJ-II Enh = 0,25 from experimental data [1].

From [1] most of the stellarators have Enh ~ 0.5

   University stellarators, with less resources, tend to have lower enhancement factors. The reason could be a more imperfect confinement. For example microinstabilities in the small Cleo stellarator gave reductions of TauE as higher as 70-100 [9].


   Resources and knowledge are much more restrictive in a home-made stellarator so a maximum Enh = 0.1 and a minimum Enh = 0.01 is considered. A medium value Enh =0.05 is taken for calculations.


   Calculations in UST_1


  Some scenarios are calculated and analysed:


T R a <ne> Enh Iota ISS04 P ECH
eV m m-3     micros W
A 10 0,1125 0,03 1E+17 0,05 1 0,052 20000
B 5 0,1125 0,03 1E+17 0,05 1 0,186 2700
C 2 0,1125 0,03 1E+17 0,05 1 0,954 210
E 2 0,1125 0,03 1E+18 0,05 1 0,692 2900
F 2 0,1125 0,02 1E+17 0,05 1 0,295 300

  Table 1




Estimation of the heating system



  In order to manufacture the vacuum vessel, a rough idea of the heating system is necessary.


   ICRH is not considered due to the big antennas.

   NBI is not possible due to cost and complexity.


ECH is the only alternative. For Bo = 0.1T , value calculated in [10], we have:


Electron cyclotron frequency = 2.8GHz. (For B=0.5 it is 14GHz)

Cut off density ~ 2x 10^17


  In WEGA  a simple  heating system is described [7]. They use a 2.45GHz magnetron which has the same frequency as the one in a commercial microwave oven. This is supposed to be the cheapest alternative. Some data reflects a cost of 2 - 4$ per watt injected by means of scientific generators. This cost is excessive.

   Bo = 0,0875 is selected in [7], maybe, to obtain 2.45Ghz as electron cyclotron frequency.

    A metallic circular tube is used as a waveguide, sometimes with a modified tip. Diameter of the tube towards the chamber  = 85mm. Power of the system  = 6kW.  





   * ECH is the only heating candidate. One or two 40mm diameter ports should be sufficient for one or two 1kW emitters.

  * Alternative F is the most feasible. In the others the minor radius "a" is scaled with CTH plasma but this optimised wide plasma has not been obtained yet for  UST_1 [11]. One or two 1kW standard magnetrons will suffice (supposition P inyected / Pabsorbed = 10% -20% ). Heating should be possible at 1 x1017m-3, having little influence the cut off frequency . Higher densities would need mode conversion [6].

  * Table1 shows that notable increments in T or "ne" cannot be achieved even installing 4 * 1Kw magnetrons.



Further developments


   The heating system will be further studied and built.




[1] Stellarator news , n 92 , May 2004

[2] Design and construction progress of the compact toroidal hybrid" Hartwell, G.J., Knowlton, S.F. Watts, C.Hanson, J.D., Brown, T.

[3] "Study of Impurity Influx of H-mode Plasma in Hot-Cathode-Biasing Experiment in the Tohoku University Heliac" , TANAKA Yutaka, KITAJIMA Sumio, et al.  J. Plasma Fusion Res. SERIES, Vol. 6 (2004)

[4] "Study of Magnetic Fourier Components Effect on Ion Viscosity in Tohoku University Heliac" , S. Kitajima, H. Takahashi, Y. Tanaka, et al. . Stellarator workshop 2005

[5] Stellarator news , n 54 

[6] "First results from the WEGA stellarator" J. Lingertat, K. Horvath, H. P. Laqua, M. Otte, Y. Podoba, F. Wagner

[7] "Electron cyclotron heating at the WEGA stellarator" Y. Podoba, K. Horvath, H.P. Laqua, J. Lingertat, F. Wagner

[9]  "Fusion research",  Dolan , Chapter 14A,  pg 405

[10] Forces on HF coil of the first outline of the UST_I    Vicente M. Queral . See  All Past R&D"

[11] Influence of coil misalignments and manufacturing errors in magnetic surfaces , Vicente M. Queral . See  All Past R&D"

[12] "Stellarator and heliotron devices", Masahiro Wakatami,    pg 401




Last Update 19-11-2005