Target wheel eddy current modelling

1. Target wheel eddy current modelling James Rochford On behalf of the Helical collaboration STFC Technology

2. Carmen–Electra comparison • Description • Having under stood the Electra solutions and gained some confidence in the solution a Carmen model was constructed which included the spokes • The CARMEN solver, has the capability to solve the full dynamic problem i.e the motion coupled to the electromagnetic solution and does not need any rotational symmetry in the problem. • A sacrificial mesh layer , “the gap” around the rotating region is re-meshed for all points in the solution • Meshing needs to be adequate to model current distribution and robust enough to allow the gap to be re-meshed at all points in the solution whilst giving consistent solutions Mesh distribution in wheel

3. Carmen–Electra comparison • Description • Having under stood the Electra solutions and gained some confidence in the solution a Carmen model was constructed which includes the spokes • The CARMEN solver, has the capability to solve the full dynamic problem i.e the motion coupled to the electromagnetic solution and does not need any rotational symmetry in the problem. • A sacrificial mesh layer , “the gap” around the rotating region is re-meshed for all points in the solution • Meshing needs to be adequate to model current distribution and robust enough to allow the gap to be re-meshed at all points in the solution whilst giving consistent solutions Mesh distribution in wheel

4. Carmen–Electra comparison • Model results; part revolution 0o-60 o • Run a number of Carmen solutions to look at the effect of step time on the problem solution • The effect of time not so critical can see step 2deg starts to deviate from 1deg solution- problem computationally very expensive. • In these solutions we see the force increases by a factor of 7 @ 100rpm w.r.t the Electra simple wheel rim prediction. • Is this real is it caused by the spokes? • Retarding torque predicted by CARMEN for 100rpm for a part revolution

5. Carmen–Electra comparison • Model results; full revolution • Here a full rotation is run But the solution step is every 2 deg but the mesh is slightly cruder • So solution not quite as accurate as part solutions • But you can clearly see 5 equally spaced peaks in the torque • Rem; wheel has 5 spokes • Between peaks Torque drops to a value comparable with the Electra solution. • Retarding torque predicted by CARMEN for 100rpm for a full revolution

6. Carmen–Electra comparison • Model results; full revolution • Here we see the torque peaks correspond to each point a spoke crosses the –ve X axis i.e. when a spoke passes through the coil centres 90o 162o 18o rotation 234o 18o 162o 234o 306o 90o 306o • Retarding torque predicted by CARMEN for 100rpm for a full revolution Alignment at t=0

7. Carmen–Electra comparison • Why does the torque increase? • The reason becomes evident once one looks at the eddy current distributions • What happens is the spokes rotate they create additional current paths, all the paths meet in the center and return via the central spoke it passes the coil centre. • This current gives rise to large Ix (~600A) along the spoke coupled to the BZ field generates a large Fy giving rise to a larger retarding torque. • In between the spoke transit the current distribution reverts to one similar that seen in the Electra models. In this case the currents down the spokes are ~80 amps and the torque generated by each spoke should cancel. I-1 I-2 I-0 I-3 I-4 I-0=I-1+1-2+I-3+I-4=590A I-1=I-4=265A 1-2=I-3=30A

8. Carmen–Electra comparison • Movie showing eddy currents a wheel rotates • Note the increase of currents in the R.H.S of the wheel as the spoke passes the coil centerline

9. Carmen–Electra comparison • Off axis torques Tx • By symmetry there should be no torque about the X axis. • This is what the models show

10. Carmen–Electra comparison • Off axis torques Ty • There may be a torque about Y causing the wheel to “jitter”. This could be generated by a nett Fz in the interaction region. • The models indicate there may be a significant Ty, • However the full revolution model (purple curve) seems to be too crude to resolve this, but the more accurate part revolution models seem to show something • It looks like we generate ~+(2-3)N.m as the spoke approaches the coil centre and switching to –(2-3)N.m as it recede from the coil centre • This is small @ 100rpm, and should scale with the speed, I would expect ~+/-(40-60)N.m @2000 rpm . • This is not huge, I may cause the wheel to jitter? • Additionally over time it may cause significant wear in wheel bearings, particularly at higher speeds?

11. Carmen–Electra comparison • Power dissipation • Whilst Electra predicts a power of 0.07kW to continually drive the wheel rim through the field @ 100rpm. • Carmen predicts additional power of 0.32kW is needed by the spokes as they pass through, creating peaks of .39kW. • This increases the average power to something like 0.2kW • i.e. more than double the Electra prediction

12. What happens at higher speeds? • Previous work to validity Carmen solution at lower speed • Now extent the model to look at Higher speeds • Look at the skin effect • Force predictions for higher speeds @ Bgap 0.485T • Power predictions for higher speeds @ Bgap 0.485T • Are previously suspected off axis forces significant • Greater immersion depths • In these model just the rim is immersed in the field • Need to quantify the effect of immersion depth

13. What happens at higher speeds? • Is the model adequate to replicate high speed operation • Is skin effect significant in models • Simple estimate of skin depth • 1/S(s.f.muo.mu.p) where • f=freq, muo=Magnetic permeability • mu =relative permeability, s=conductivity • Full field penetration of ring out to 6000rpm • Still significant dragging of the field • No special mesh considerations • Other mesh issues • Pecklet number • Insufficiently small mesh may prevent convergence in solution. • To avoid this need Pecklet number <1 • Mesh in outer region of wheel <4mm

14. What happens at higher speeds? • Predicted power dissipation @ different speeds • Models run for gap field of 0.48T • At 2000 rpm torque peaks at 7.7kWm

15. What happens at higher speeds? • Predicted power dissipation @ different speeds • Models run for gap field of 0.48T • At 2000 rpm power peaks at 7.7kWm

16. What happens at higher speeds? • Are off axis torques significant? • No indication of off axis torques • Would expect them to scale with speed • Don’t see this • Probably just a mesh error

17. What happens at higher speeds? Plot of Bz on field surface at 2000rpm Rotation • Is there significant field distortion at high speed • The field is dragged • this may be significant for beam\pair production? • There are two effects • general dragging related to speed • And a periodic distortion from spokes Field plots

18. What happens at higher speeds? Dragging as a function of speed • Field distortion by rim motion • The field is dragged • Normal cylindrical distrobution of Bz • Distorted along the direction of motion • This is constant at constant speed • So may not be a problem

19. What happens at higher speeds? • Field distortion by spokes motion • Get a periodic jitter in the field • This may be an issue for the beam pair production • Here see the effect of a spoke passing • @ 54 deg mid point between spokes • @ 90 deg spoke center passing • @126 deg next mid point between spokes • See here the field wobbles as the spokes pass 90o 162o 18o 234o 306o

20. What happens at higher speeds? • Additonal models to run • Running high speed models at higher field • The current models are at 0.485T • want to run 1 200rpm model at 1T as per ILC wheel • Quantify the effect of immersion depth • In these model just the rim is immersed in the field • 1-2 high field models with different immersion depths • Agreement between models and experiment