Optimum Iota Profiles    



Abstract : The present ideas about the adecuate Iota profiles for UST_1 are described. The iota profiles of some devices are analysed. The definition and optimisation of magnetic coils depends, among others, on Iota profile.

 Torsatron versus classical-modular  stellarators

 Some properties of each device related or not with Iota are:


   * Tend to have steep Iota profile. So it creates  several low order rational surfaces. For example in LHD, [3],  and in less degree in CTH, [4] page 14. However the magnetic islands are smaller due to the magnetic shear, W = width of islands = ( Berrors / S) , Berrors = resonating magnetic field errors , S = magnetic shear [1].

   * They need poloidal coils to compensate the net vertical field generated by the helical fields. This is an additional complexity.

   *  May require the control of the poloidal field according to the plasma beta to maintain good confinement [2] and try to fix the plasma boundary. The last is important when divertors are used and can be deduced from [2] and [3].


  Clasical stellarators- modular

   At the present classical stellarators are mainly represented by modular stellarators of the type helias (W7-AS, W7-X) or quasi-symmetric (HSX, NCSX)

    * They can avoid all low order  rational surfaces.

   * However shear is low so the size of the magnetic islands is bigger for the same rationals.

   * Higher simplicity due to no poloidal coils and control.

   * The coils can be repaired more easily.

   * It is possible to design a coil system that gives a stiff magnetic field, [3], like in W7-X. For the future reactors it is an advance.

   * Nearly all new stellarators are modular.

   * On the other hand the coils are more complex and expensive than, perhaps, the helical coil of a torsatron.

   * The quality of some parameters (confinement time...) of an old modular stellarator like W7-AS seem similar to the new superconductor LHD [3].



 Iota profile in stellarator and heliotron devices


* W7-X . Flat iota profile. From 0.87 (r/a =0) - 0.98 (r/a =1). Little variation with Beta. [3]

* TJ-II . Flexible but relatively flat iota profile. One tipical configuration is around Iota= 1.5 [1]. In [5] Figure 6 appears several configurations. The case Iota = 1.51 - 1.60 is free of low order rationals.

* W7-AS . Flat iota profile around 0.5 [3]

* NCSX . Flat Iota profile from the external magnetic fields. Iota : 0.44 - 0.49 . [6] page 12 and [1].

* LHD .  Steep Iota profile. Iota :  0.5 - 1.1 for Beta=2.5%

* CTH .  "Medium" Iota profile. Iota :  0.38 - 0.48 for TF= 0.34. [4] page 14.


   Most of the devices, except for heliotrons, have been design to ocupy the gaps between  the low rationals  numbers. In Graph 1 and 2 this gaps are represented.



   The energy confinement time in stellarators is proportinal to  ι0.4  acording to  ISS95 scaling  and ι2/30.47  in ISS04v1  [7]. So this possitive though reduced influence have to be considered.


    The reason for the not use of higher Iota, for example 2, is not clear, but the stability against m=1 kink modes, the limit q<2 in tokamaks and the Greenwald Limit might have some relation.


   Other parameters like the optimum (cost, engineering issues) bending of modular coils could limit Iota to the  regions near 0.5 or 1. It is supposed that without a deep bending of the coils a high rotational transport cannot be achieved. In the limit, with planar coils, only toroidal field will be obtained, Iota = 0.




Further developments


   Further knowledge or the help of one expert in optimization is necessary.



[1] "STELLARATORS" , D.A. Hartmann, Max-Planck Institut für Plasmaphysik.

[2] "Stellarators and heliotron devices", Masahiro Wakatani. Oxford University Press. Pg 264

[3] "Significance of MHD EffectsSignificance of MHD Effects in Stellarator Confinement", Arthur Weller et al. 15th INTERNATIONAL STELLARATOR WORKSHOP, 2005

[4] "MHD stability studies  of current-carrying plasmas  in the CTH" , S. F. Knowlton, G. J. Hartwell et al. Auburn University, Auburn

[5] "Confinement studies in the TJ-II stellarator" C Alejaldre, J Alonso, L Almoguera, E Ascasıbar et al.

[6] "The Promise and Status of Compact Stellarators" , Hutch Neilson, Fusion Power Associates Symposium 2004.

[7] "Confinement study based on an extended international stellarator database"  , Stellarator News, May 2004




Graph 1.  Iota gaps for n, m modes







Graph 2 .  Iota gaps for n, m modes. Low Iotas. 














Last Update 26-10-2005