Abstract : The planned system, calculations and design of the heating system for UST_1 is described. It is based on a commercial magnetron at first or second harmonic at 2.45GHz.

                       Previous calculations

   Some previous general calculations were done in [1] , "Energy confinement time and estimation of the heating system in UST_1"
 

   The main points in that publication are:
    

* A comparation between the real and theoretical value of energy confinement time in CTH  , TU-Heliac  , W 7-AS , WEGA  , TJ-II  is carried out to test the expressions. ISS04 and ISS95 is compared.

* Enhancement factors of 0.1 to 0.2 are observed in medium quality university stellarators. Enhancement factor = 0.05 is taken as a first approximation for UST_1.

* Max. plasma temperature : UST_1 could reach 2eV if 1Kw of heating power is used asuming 30% of power absorbed. This value seems very optimistic now. Additionally only 1.6 x10^-18 Pa  of residual gases has been achieved and the previous data is for 1x10^-17 Pa of hydrogen. At 1x10^-18 Pa , for Hydrogen, 2900W of absorbed power is necessary what is an enormous power for this small stellarator. Only if the enhancement factor could reach 0.1 or 0.2 the system will be more favourable. However in Cleo, an old and small but serious stellarator, sometimes an enhancement factor as low as 0.01 was obtained due to instabilities. UST_1 might be worse than Cleo.

* No higher T can be obtained. 20Kw of absorbed power is necessary to obtain 10eV  at 1x10^-17 Pa.

      Some new additional calculation and data

*  Cut-off frequencies :  Three cases are analysed because the  magnetic field strength will be increased progressively. Case B =0.087 T , 0.043 T and 0.029 T

corresponding to fundamental, second and third harmonic is calculated. Following the expressions in [2] and contrasting with Dolan the results for  2.45 GHz are :

O-mode cut-off density :  0.8 x 10^-17 m^-3

High density cut-off for X-mode :  1.5 x 10^-17 m^-3 for B = 0.087 T

1.15 x 10^-17 m^-3 for 0.043 T

1.0 x 10^-17 m^-3 for 0.029 T

So in any case the cut-off density is around the order of 1 x 10^-17 m^-3  (not 1 x 10^-18 m^-3 = the present minimum pressure in the chamber)

- The upper hybrid frequency is higher than cyclotron frequency.

   * Antenna design : 

   The most simple antenna for this frequencies is a waveguide with or without a special end.  Different antennae are described for example in WEGA stellarator [3] [4].

   However UST_1 is so small and the port was manufactured without knowing anything about the heating system for UST_1 that even the mode TE10 cannot penetrate through the port. At least a 62mm rectangular waveguide is necessary. Rectangular waveguides are calculated by means of a code from  Mustafa Demirhan and Sinan Gezici [5] . The propagation in waveguides and vacuum is visualised with  "falstad" code [6]

Two solutions are planned: a) the use a medium with high dielectric cte. , for example glass, that will allow the penetration of the waves into the vacuum vessel  b) The use a coaxial line and a stub or strip antenna.

Option b) will be the fist tested. The cable, power connectors and microwave are already available. Type N connectors are suitable for 300W CW and perhaps 1kW pulsed regime at 2.45GHz. Cable is RG-214, low loss and high microwave isolation. Some doubts remain for example how to design a matching device from 50 Ohm to less than 50 Ohm (5-20 Ohm) due to plasma effect.  The use of a commercial microwave to heat (pre-ionization in this case) plasma is perfectly described in [7] relative to the Korean Tokamak.

* Heating and Mode Conversion : My knowledge of plasma heating is very limited and it is based on several publications and Dolan information.

From [3] it is clear that results will be very poor. In WEGA stellarator they reach for the first experiences a best case  ne = 2 x 10^-18 m^-3 and Te = 4eV for an advanced heating procedure. Even here the temperature profile is hollow. a) They launch the waves in the correct direction (45º) to achieve a notable O-X mode conversion (about 10%) and these X waves will suffer OXB conversion (converted into Bernstein waves following the paths shown in  [4]). Finally they achieve more than 10 times the O-mode cut-off density =  0.8 x 10^-17 m^-3

  b)  However if only O-mode and small OX conversion is achieved because the emission angle is 90º , density achieved was only 1.5 * density O-mode cut-off. Hollow profile (ne and Te are higher out of the LCFS than at the plasma centre). The plasma is heated by multiple reflections between the cut-off layer and the vessel walls.

  c) If X-mode , 90º antenna, is used, only less than the density for the X-mode cut-off was possible, very hollow profile and  plasma instabilities.

   In UST_1 where the first antenna will be a stub 1/4 * wavelength = 3cm and with a vacuum vessel so small that acts as a waveguide capable to maintain only the mode TE-10 (the other are evanescent waves) the result is totally unknown. Not even clear if the O-mode or the X-mode will prevail. In the best scenario the waves will suffer multiple reflections and will heat the plasma at the edge. It would be a great success. Heating the plasma centre will be a further development.

   It is clear that the best solution is to work below the cut-off density but it will be only possible when the probable small leak was sealed. An ebay low cost RGA system is being shipped to solve this issue and to have information about the gases in the chamber. 

   Main ideas

   Plasma heating might be possible at 2.45Ghz from a commercial magnetron oven but the plasma profile will be hollow if density do not reach 0.8 x 10^-17 m^-3 .One 800W magnetron is enough for the first experiments.
 

Further developments

   The heating system will be built.

 References

[1] "Energy confinement time and estimation of the heating system in UST_1" Vicente M. Queral . See  “All Past R&D"

[2] "Electron Cyclotron waves" J. A. Hoekzema , Transactions of fusion science and technology , vol 45  mar 2004

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

[7] "Simple microwave preionization source for ohmic plasmas" W. Choe et al. REVIEW OF SCIENTIFIC INSTRUMENTS VOLUME 71, NUMBER 7.

Last Update 19-07-2006