1. 1 DWS- SOFT 9-04 1. Load tolerant matching Evaluated the conjugate tee configuration in plasma conditions Strong current imbalance between the straps was observed Load tolerant behavior not readily obtained with strong coupling between straps Initial results from phased ICRF operations on Alcator C-Mod

2. 2 DWS- SOFT 9-04

3. 3 Evaluated the system in plasma conditions The currents and forward power for each straps (1-2-3-4) are strongly affected when changing the stubs lengths. Observed strong current imbalance between the straps Current ratio can be up to 2 No degradation of heating efficiency or increased impurity production was observed. Initial test on E-antenna

4. 4 DWS- SOFT 9-04

5. 5 Current imbalance is predicted by transmission line models Due to changes in the inductive loading Intrinsic to the configuration With strong strap-to-strap coupling, the loading impedance is affected Compact antenna design in C-Mod  strong coupling between straps For E-antenna up-down coupling (same strap) : -7dB adjacent straps : -20dB Bottom figure shows how the loading impedance at the antenna ports changes as the stub lengths are varied As a result of these two effects, load tolerant matching was not obtained on E-antenna Current imbalance and strong strap-strap coupling

6. 6 DWS- SOFT 9-04 Used transmission line model to evaluate the approach for J-antenna Reference case, symmetric stub lengths. This shows typical load variations as seen by the generator. Conjugate tee system without strap-to-strap coupling : resilience to loading variations is obtained. Conjugate tee system with strap-to-strap coupling : the load tolerant properties are lost. Only two non-adjacent straps are powered. The other two straps are not powered but taken into account. Level of coupling between straps for J-port: adjacent straps:-8.5 dB non-adjacent: -20dB / -32dB Load tolerant matching using non-adjacent straps in a strongly coupled four- strap array is not readily obtained Strong current imbalance is also seen  phasing control is lost, compatibility with flexible phased operations is not guaranteed Evaluation for the four-strap J-antenna

7. 7 DWS- SOFT 9-04 Model for J-port antenna

8. 8 DWS- SOFT 9-04 Strongly coupled 4-strap antennas 4 current straps “Hairpin” strap configuration One exists in C-Mod now Another is being designed Feed point Ground Current strap side view Antenna being designed Existing J-port antenna C-Mod – Effects of mutual coupling on load-tolerant antennas

9. 9 DWS- SOFT 9-04 Antenna transmission-line model is used to compare with experiment Each “hairpin” is modeled using 8 lengths of transmission line Line segments representing the plasma-facing elements have: –Mutual inductive coupling with k 21 ≈ 0.12, k 31 ≈ 0.033 –Phase velocity ≈ 0.55c (from Faraday shield capacitive loading) –Loss from plasma coupling R’ ohms/m Other lines do not have mutual coupling –Checked with earlier modeling with mutuals for all lines; we found that adding the (small) mutuals didn’t make significant changes. Striplines connect back of hairpins to coax Stripline Plasma-facing coupled lines

10. 10 DWS- SOFT 9-04 Results with no coupling are standard - no surprises Pick value of Z match (impedance to match to – determines impedance of quarter-wave transformer (QWT) Set lengths of lines h6a and h6b to provide exact match at nominal loading (10  /m for C-Mod) Observe standard load-tolerant behavior Specific antenna cofiguration not critical –Hairpin antenna OK –Straight antenna OK |  | vs R’ (  /m) f = 50, 70,80 MHz Z match = 10  Simple linestretcher matching |  | vs R’ (  /m) f = 50, 70,80 MHz Z match = 20 

11. 11 DWS- SOFT 9-04 Add mutual inductances determined from present J-port antenna Inductive coupling coefficients (M ij /L) k 12 = 0.12 k 13 = 0.033 k 12 and k 13 values based on measured S-parameters of J-port antenna Comparison of measured and calculated values of S 12 and S 13 for J-port antenna P. M Ryan, Oxnard (2001)

12. 12 DWS- SOFT 9-04 Can we use external decouplers to regain load-tolerant behavior? Load-tolerant matching properties are lost with large values of inter-strap coupling. Can we use simple decouplers external to the vacuum vessel to counteract nearest-neighbor coupling, and will this allow load-tolerant properties? External circuit - Lines of length h5 (Z = 50  ) from striplines to decoupler location Decouplers –cross lengths hx are fixed –stub length hs can be changed when frequency is changed

13. 13 DWS- SOFT 9-04 Set the decouplers At each point along the lines, there is a 4x4 admittance matrix (Y-matrix) Set decoupler lengths: Choose h5 so that Y 01 is almost completely imaginary Determine hx and hs so that – Im(Ydec 01 ) = – Im(Y 01 ) and – Im(Ydec 00 ) = 0

14. 14 DWS- SOFT 9-04 Set lengths h6a and h6b from decouplers to junctions to match at ref. loading Procedure: Calculate 2x2 S-matrix at the two junctions as functions of h6a and h6b (note: things are symmetrical) Adjust h6a and h6b so that S 00 = 0 (real and imag. parts) Scan R’ over 4  /m < R’ < 40  /m; look at S 00 and S 01 as R’ is changed. Changing value of Z match will change load- tolerant properties of system, so try for different values of Z match. Look at frequencies f = 50, 70,80 MHz

15. 15 DWS- SOFT 9-04 Results for decouplers close to antenna are not bad For Z match = 10 , S 00 shows good load-tolerant behavior at 50 MHz, For Z match = 20 , S 00 shows good load-tolerant behavior at 70 MHz S 00 for 50, 70, and 80 MHz S 01 for 50, 70, and 80 MHz h5 = 0.14 m Z match = 20  h5 = 0.14 m Z match = 10 

16. 16 DWS- SOFT 9-04 More exacting constraint is to look at reflection coefficient when both lines are powered Put equal powers into both inputs with specified phase angle h5 = 0.14 m Z match = 20   = 180° h5 = 0.14 m Z match = 20   = 90°

17. 17 DWS- SOFT 9-04 BUT - we can’t put the decouplers near the antenna! Must have h5 > 1m, so that we can make the decoupler connections outside the port. Question: can we find a single location for the decouplers (i.e, one value of h5) so that system will work as well as in previous example Answer: haven’t found it yet, and I’m not optimistic. |Y 5 | f=50 MHz |Y 5 | f=70 MHz |Y 5 | f=80 MHz Admittance matrix on source side of decouplers for h5 = 0.14 m Note that all off-diagonal components are small.

18. 18 DWS- SOFT 9-04 Increasing position of decouplers by /2 works - for that frequency Example: h5 increased by  /2 at 70 MHz, h5 = 2.283 m S 00 for 50, 70, and 80 MHz S 01 for 50, 70, and 80 MHz For f = 50 and 80 MHz, large S 01 destroys match and load tolerance

19. 19 DWS- SOFT 9-04 Conclusions for C-Mod antenna with strong coupling Load-tolerant behavior can be obtained using highly coupled antenna straps with external decouplers and matching systems. Because of the length constraints on decoupler connections, up to 13 components need to be changed when changing frequency: 4 antenna-to-decoupler lengths, h5 3 decoupler stub lengths, hs 2 decoupler-to-junction lengths, h6a 2 decoupler-to-junction lengths, h6b 2 quarter-wave-transformers (QWT) –these transform Z match to Z line (char. imp. of the main transmission line) –need to change inner conductor to change Z match, and also to make transformer length /4 for the frequency desired There may be a better way to obtain load-tolerant behavior. This is a very active area of investigation now. Stay tuned...