Volodymyr Kyrytsya LPP, ERM-KMS Brussels

1. Volodymyr Kyrytsya LPP, ERM-KMS Brussels E// distribution in front of one triplet of ITER ICRH antenna, its sources and role of the Faraday shield.

2. Motivations. Geometry of the antenna under study. Boundary conditions. Quasi magneto-static approximation (QMS). Fields distribution in front of the antenna with no FS. Fields distribution in front of the antenna with FS. Currents on the FS. Interpretation of the return currents. Conclusions. Outline of presentation

3. What we try to do: Simulate E// distribution near the antenna by MWS. Emplane E// sources and distribution by suitable analytical model. Understand role of the FS. Suggest guidelines for E// optimisation. Motivations. • What is the problem: • Some simulations show that sheath effect may be a problem in ITER ICRH antenna. • E// is the cause of the sheath. • E// should be minimised in front of the antenna.

4. One triplet of the ITER antenna and coordinate frame. X - radial Y - poloidal Z - toroidal Frequency = 47.5 MHz Load – Vacuum or dielectric with Eps=10 or Esp=100 located at 2-6-10cm from FS . Feeded by 1Wat of incident power at 4P junction. Bisected by XY plane. Boundary conditions: antenna radiates through the aperture in infinite ground plane (not shown).

5. MWS simulation solves numerically complete set of Maxwell equations for the model. But for interpretation of the result we need analytical description. In the antenna box and near the aperture fields can be described by Maxwell equations in vacuum with suitable boundary conditions. Approximation used used for interpretation of the results. (1) (2) We assume that B field near the straps is mostly defined by the currents and displacement current can be neglectedin first approximation. Electric field can be calculated afterwards from the complete equation (2). This is quasi magneto-static (QMS) approximation.

6. Simplified equations used for interpretation of the results. In the first approximation B-field is created only by currents on antenna. (4) In the second approximation we calculate E-field from known B-field distribution. (5a) EZ is defined by the change of BX along Y and by the change of BY along X. B is defined by the currents (4), thus relations between E and currents on the antenna can be established! (5b) (5c)

7. Current and magnetic field distribution. max(Jpol)=2.1 A/m poloidal currents max(Jtor)=1.66 A/m toroidal currents In the first approximation magnetic field is created by strong poloidal current on the straps. Bz,Bx>>By everywhere.

8. Justification of the quasi magneto-static approximation. Quasi magneto-static approximation is justified for the problem if magnetic energy >> electric energy in its domain. max(Wmag)=4.2e-8 max(Wel)=6.8e-9 Electric energy near box aperture. Magnetic energy near box aperture. Magnetic energy >> electric energy near aperture and almost everywhere inside the box (not shown here) thus we can use quasi magneto-static (QMS) approximation.

9. Ez in front of the antenna with Dielectric with FS. max(Ez)=3.3V/m max(Ez)=1.1V/m max(Ez)=1.1V/m 2cm to FS 6cm to FS 10cm to FS At the distances < bar gap (d_bars) Ez is defined by the currents on the FS bars. Distances < d_bars are out of interest in this presentation. Fields at 10 cm to FS is chosen for analysis.

10. Ez, vacuum case 10cm to aperture. No FS. /J/ Bx By Ez Ez field distribution is similar to that of strip-lines short circuited at the end. On the black lines Ez is created by first term (non uniform Jy (Bx) distribution). On the pink lines at short circuits second term of the formula become important (By is created by Jz and Jx) and both terms almost cancel out making Ez~0 at short circuit.

11. Ez, dielectric (Eps=100) case 10cm to aperture. No FS. /J/ Bx By Ez With dielectric Ez is dominated by the second term in the formula. Derivative of By in dielectric is sqrt(Eps) times larger then in vacuum. Physical meaning: By component (created by Jz and Jx) tunnels trough the vacuum inside the dielectric and then excite a propagative wave with Ez.

12. By and Ez in dielectric (Eps=100) and in vacuum, no FS . By Ez /Ez/ wave wave dielectric dielectric dielectric By Ez /Ez/ vacuum vacuum vacuum

13. Conclusions about Ez for the case with no FS. • For antenna in vacuum Ez distribution in front of the antenna is mostly defined by the dBx/dy thus by Jy currents on the straps. At the short circuited ends of the straps Ez~0. • For antenna in front of dielectric/plasma Ez distribution is dominated by the dBy/dx thus by Jz currents on the box edges. These currents are closest to the dielectric and radiate into it creating propagative wave with By and Ez.

14. Vacuum Eps=10 Eps=100 Ez in vacuum and dielectric with and without FS, d=10cm. /Ez/max=5.56 v/m /Ez/max=2.03 v/m /Ez/max=1.97 v/m /Ez/max=0.28 v/m /Ez/max=1.84 v/m /Ez/max=1.98 v/m

15. Conclusions about Ez for the case with FS. • For antenna in vacuum Ez distribution in front of the antenna is mostly defined by currents on the straps. FS cover the straps and screens out almost completely Ez. • For antenna in front of dielectric/plasma Ez distribution in front of the antenna is mostly defined by the currents on the box edges. FS are absent over this area and its presence makes almost no difference for Ez distribution.

16. Ez and By on the XY plane. /By/ /Ez/ Jz on bars and on box edge are of the same order but Jz on FS does not create Ez.

17. Dominant currents are in toroidal direction. Fringing currents are 5-10 times less intense. Currents on FS are established in order to satisfy boundary conditions on the PEC surfaces: B_perp=0 E_tan=0 The dominant currents on the FS are induced by Bx. Currents on the FS. It can be shown that B_y produced by one Jz current on the bar is cancelled by the neighbouring currents from left and right at the distances to FS > d_bars. This is not the case for last current and this last edge current generates By and can radiate Ez. Suggestion1: Keep vacuum gap >= d_bars. Suggestion2: Cover box edges with FS like bars...? Does not work as good as expected...

18. Normal, attached bar, castellated, or extended FS? None of this geometries provides radical reduction of /Ez/... /Ez/max=1.98 v/m /Ez/max=2.15 v/m /Ez/max=1.82 v/m /Ez/max=1.80 v/m

19. Jz responsible for Ez. Interpretation of return/image currents. On the box edges return/image currents are the cause of Ez. These currents on the box are necessary to eliminate normal (to the PEC surface) component of the B produced by antenna without box. Aligning box surface as much as possible with magnetic field lines will lead to reduction of these return/image currents and Ez.

20. Distribution of the E// around antenna were simulated with MWS. Connection between of E// and currents on the antenna established in frame of QMS approximation. E// in front of the straps can be effectively eliminated by FS (at the distances larger then d_bars). E// in front of the box edges is created by edge currents. Lowering the edges (if possible) will lead to reduction of E//. E// in front of box edges may be diminished by alining box walls with magnetic field lines of the antenna thus reducing “return currents”. Modeling is needed. Extended over box edges FS can not effectively reduce E// created by Jz on the box edges. Developing of approximate analytical description of the FS is under way. Conclusions.

21. Acknowledgements. I gratefully acknowledge fruitful discussions and suggestions from many colleagues from my laboratory: Roger Weynants, Frédéric Durodié, André Messiaen, Raymond Koch, David Faulconer, Dirk Van Eester, Georgette Van Wassenhove, Pierre Dumortier, Mark Vrancken, Fabrice Louche.

22. Additional slides.

23. Justification of the quasi magneto-static approximation. Quasi magneto-static approximation is justified for the problem if magnetic energy >> electric energy in its domain. max(Wel)=6.0e-8 max(Wmag)=4.9e-7 Electric energy near box aperture. Magnetic energy near box aperture. Magnetic energy >> electric energy near aperture and almost everywhere inside the box (not shown here) thus we can use quasi magneto-static (QMS) approximation.

24. By and Ez in dielectric (Eps=100) and in vacuum, no FS . dielectric dielectric dielectric /By/ Phase(By) /Ez/ vacuum vacuum vacuum

25. Electric and magnetic energies. We can use eddy current (quasi magneto-static) approximation for the problem if magnetic energy >> electric energy in its domain. Magnetic energy near box aperture. Magnetic energy + Electric energy near box aperture Total energy is dominated by magnetic energy near aperture and almost everywhere inside the box (not shown here).

26. Explaining why FS does not create By and does not radiate Ez. In order to compensate Bx created by straps and make it =0 on front and back surfaces of each bar, edge currents along Z are established (see previous slide). B_y produced by one current is cancelled by the neighbouring currents from left and right at the distances > d_bars. This is not the case for last current and this last edge current generates By and can radiate Ez. On the box edges currents along Z play the similar role of compensating strong Bx on PEC surface, but they do not have neighbours to compensate theirs By and can radiate Ez. Suggestion1: Keep vacuum gap >= bar width. Suggestion2: Cover box edges with FS like bars...? Does not work as good as expected...

27. All fields in front of the antenna in vacuum with FS. Magnetic fields Bx,Bz>By max(Bx)=0.08A/m max(By)=0.04A/m max(Bz)=0.07A/m Electric fields Ex,Ey>>Ez max(Ex)=5V/m max(Ey)=9V/m max(Ez)=0.3V/m

28. All fields in front of the antenna with dielectric with FS. Magnetic fields Bx,Bz>By max(Bx)=0.09A/m max(By)=0.04A/m max(Bz)=0.11A/m Eps=100 Electric fields Ex,Ey>Ez max(Ex)=11V/m max(Ey)=6V/m max(Ez)=2V/m

29. max(Bx)=0.09A/m max(By)=0.08A/m max(Bz)=0.09A/m All fields with anisotropic dielectric Eps=(50,50,10000), no FS. Bx,Bz>By max(Ex)=11V/m max(Ey)=7V/m max(Ey)=0.2V/m Ex,Ey>>Ez