Sensitivity to demagnetization Brooks, Stephen Georg Heinz Hoffstaetter ; --[thanks a lot. So our limit is 1kGy hitting one block? Lets assume one block weighs about 12g, the block can then take 12J of lost electrons.]-- Well, the 1kGy limit is for the radiation hitting everything, with a very safe field deterioration of a few "units" or parts in 10^4. A typical whole magnet (QF) has 5.14kg of NdFeB material, so that would be 5.14kg*1kGy = 5.14 kJ. The "one block down by 1%" example scenario I modelled would need at least 74kGy on that block. The "block" in this case is a column of 2 blocks in that location, total mass 321 grams. 0.321 kg * 74kGy = 23.7 kJ. So the energy loss limit in a single magnet is a few kJ either way. The 2nd example having a marginal field quality. --[With a beam energy of 6MW, we could deposit one millionth of the beam, i.e. one nA, in one block for 2 seconds, if all the electrons energy stayed in the block. That is a very short time for a very tiny loss. Do you have an estimate of how much of the electron energy remains in the block for a 150MeV electron?]-- I don't know for sure but I'd think the electrons would stop within the blocks, so would deposit all of their remaining kinetic energy. It's not quite as bad as you estimate because the limit is 100-1000x higher*. Still, that only gets us a few minutes to half an hour of 1e-6 level beam losses (at 40mA) in a single magnet. That's why it's important to monitor these levels as we ramp up current. The actual dose is no problem to detect (it's higher than human-level dosimeters), so we can see where the problem areas are. [* This is still assuming the worst H field throughout the magnet, so there may be another 10-fold increase in the limit if I use some sort of average. It also doesn't account for any absorption of electrons in the beam pipe. But these don't change the overall situation that we can't run for hours with 40mA without being extremely clean.] -Stephen Georg Heinz Hoffstaetter Tue 12/06, 18:56 Hi Stephen, thanks a lot. So our limit is 1kGy hitting one block? Lets assume one block weighs about 12g, the block can then take 12J of lost electrons. With a beam energy of 6MW, we could deposit one millionth of the beam, i.e. one nA, in one block for 2 seconds, if all the electrons energy stayed in the block. That is a very short time for a very tiny loss. Do you have an estimate of how much of the electron energy remains in the block for a 150MeV electron? Thanks a lot for your response, Georg Brooks, Stephen Hi Georg, Sorry I didn't reply earlier, my parents came visiting and I took Monday off showing them around Long Island! --[For the error analysis of a single damaged magnet it would be ok to stick to the Lou limit. Either limit would actually be fine for me as long as I can formulate it in a super simple way to the DOE.]-- I worked out in the attached spreadsheet that the case I showed: a BD with the large near-midplane block weakened by 1%, scores 0.258 on the Lou criterion. So as far as multipoles are concerned, it's not too bad. The overall quad strength error is -0.116%, although it's a lopsided BD so I don't directly use this criterion normally. I think this case with the single block weakened by 1% is roughly on the edge of acceptibility. If you use this as representative, you see that my 1000Gy (100krad) figure based on 0.02-0.03% weakening is very conservative (deliberately so). So the true limit could be a bit higher. The reason for excessive caution is that there are a few things, like the material behaving slightly differently to that in Temnykh's paper, that could change the radiation resistance exponentially. Another bad case would be if the beam damages the block on the side nearest the pipe (likely), where the damage has a proportionately larger effect due to its proximity to the beam. Another place I've been cautious is that I've used the *worst* "H" field scenario for the whole magnet, whereas in reality it varies across the magnet, so not all points are as sensitive. The reality is we probably have some leeway above the limit I initially gave, so it's a bit like an "administrative limit". I want to see we've got the procedures in place to measure radiation, detect and correct low-level losses, avoid turning up beam current massively when there are detected losses, things like that. We may even find there are sources of radiation like the cavities or dump that could do with extra shielding. Once that is straightened out, towards the end of the run we can try higher currents potentially with radiation limit negotiated upwards. As part of this negotiation I can probably do a more complex demagnetisation simulation taking into account H variation across the magnet. Maybe I can input cases of radiation calculated from a code (if you have someone who can run FLUKA or MARS for example). --[That would be fantastic :-) :-)]-- OK, so the short explanation for "demag.xlsx" is: Temnykh's data agrees with the model that the dose for a 1% demagnetisation has the following formula: Dose_1% = 10^m0 * 10^(T_demag/Tbar) (this is eqn. (12) in NIM A 587 (2008) 13–19). Here, m0=-2.68 is a fit constant to his data. T_demag is the "demagnetising temperature" of the material sample, basically the Curie temperature, which depends on how the material B-H curve changes and when the demagnetising part of the curve hits the "working point", which is determined by the local "H" field, which is determined by the material shape. So, both the material grade and geometry affect T_demag. Note that T_demag is in degC and assumes some "room" temperature (around 30C for his study, correct for CBETA too). Tbar=41.4K is another fit constant that shows the change in Curie temperature that causes a 10x decrease in radiation damage levels. This is where my "exponential dependence" comes in: a small-ish change in T_demag can make a large change in Dose_1%. For our material grade N35EH, the stated T_demag measured by the vendor is 200C. On lines 7-11 on my spreadsheet, I correct this using measured H field in the Halbach magnet (the vendor's test piece geometry had H=-0.67T, the bad corners of the Halbach has H=-1.3T). I also noted the H change per Kelvin and use this to extrapolate T_demag to the worst case in the Halbach magnet, which is 147C. Then in lines 1-5 I plug this into Temnykh's formula to get Dose_1%, which is 74kGy (7.4Mrad). I then look at the effect of doses and decided that the 1kGy (100krad) level, which produces a 0.013% field loss (like 1.3 "units"), is the level at which field loss is basically negligible. Perhaps detectible at the precision level, but can't endanger the running of the machine at all. The other reason for giving a pessimistic dose limit like that is that we can't monitor *every* point in space, so I hope that keeping the places we do monitor below that level means any hotspots we miss are reasonable (i.e. certainly not above that 74kGy=Dose_1% level) too. -Stephen Georg Heinz Hoffstaetter Fri 08/06, 15:41 Hi Stephen, between the lines ... Best, Georg On Jun 8, 2018 11:10 AM, "Brooks, Stephen" wrote: Hi Georg, --[James confirmed that as far as he is concerned, the "Lou criterion” is used to accept Halbach magnets. Is this correct?]-- Not really. At the moment I'm accepting magnets by a stricter criterion based on how good we can make them. That's 1.5 Gauss midplane field error, less than 10 units multipole "sum" FOM, and less than 0.375 on the CBETA FOM. For QF-style magnets, I also want the overall quad strength error less than 0.05%. This was done at the request of Scott Berg, who thought that there could be additional errors to do with the BPMs that were not in William's original simulations. So we halve the 0.75 error budget to 0.375, to allow for additive effects from BPM nonlinearities etc. on the same level as magnet errors. If we accepted magnets at the CBETA FOM < 0.75 level, my feeling is that it would "probably" work, but if possible, we want an even better level of confidence. I think that's great, having all magnets a bit better than the limit is very recommendable. For the error analysis of a single damaged magnet it would be ok to stick to the Lou limit. Either limit would actually be fine for me as long as I can formulate it in a super simple way to the DOE. --[b) If we had a perfect magnet, and the strongest pole changes by …%, we barely stay within the acceptance criterion.]-- Do you mean pole or permanent magnet block? Either way, this isn't necessarily the sort of errors we would get in reality. The demagnetisation could be anything from uniform (if the radiation is from a far source, e.g. shining off the dump or RF), to very concentrated at one point. The PM block arrangement does not affect it. My assumption is that the worst field deviation happens 1:1 from the magnetisation deviation. This is exactly true for uniform irradiation and a little pessimistic for localised demagnetisation. I mean one block. Having mostly a midplane block damaged is very likely, because energy deviating losses happen in this plane and are probably dominating. And that's the question the DOE asked. --[c) Pervious studies show that … deposition of several MeV electrons in one block will lead to approximately this change in magnetization.]-- If you use the 1:1 rule above, this is given in my demag.xlsx spreadsheet although admittedly I only wrote it for my own use so it's a bit cryptic. Do you want me to send you a written "transcript" of the reasoning for that calculation so you can sent it on? That would be fantastic :-) :-) -Stephen From: Georg Heinz Hoffstaetter Sent: 08 June 2018 09:40:11 To: Georg Heinz Hoffstaetter Cc: Brooks, Stephen; James Arthur Crittenden; Wei Yuan Lou; Berg, J Scott; Trbojevic, Dejan Subject: Re: Sensitivity to demagnetization Hi Stephen and James, James confirmed that as far as he is concerned, the "Lou criterion” is used to accept Halbach magnets. Is this correct? Since a DOE officer (Eric Colby) asked this specific question, I would really like to develop an answer quickly. Would this be possible? What I wold like to send him in a (small) nutshell is: a) We measure 18 multipoles. The acceptance criterion is … (Lou criterion) b) If we had a perfect magnet, and the strongest pole changes by …%, we barely stay within the acceptance criterion. c) Pervious studies show that … deposition of several MeV electrons in one block will lead to approximately this change in magnetization. Is it possible to produce these numbers for me? It would make a really good impression of CBETA to the DOE if I could follow up my presentation and Erics question with these numbers. Thanks so much, Georg On Jun 7, 2018, at 2:50 PM, Georg Heinz Hoffstaetter wrote: Sorry, I am still not understanding. What is now our official acceptance criterion and why? Thanks, Georg On Jun 7, 2018 2:49 PM, "Brooks, Stephen" wrote: We're doing 2-3x better than that with our magnets. Scott had some reasons for wanting to do better than that if possible. -Stephen From: Georg Heinz Hoffstaetter Sent: 07 June 2018 14:47:18 To: Brooks, Stephen Cc: Georg Heinz Hoffstaetter; James Arthur Crittenden; Wei Yuan Lou; Berg, J Scott; Trbojevic, Dejan Subject: Re: Sensitivity to demagnetization Hi Stephen, I though the criterion is what William analyzed, i.e. the rms over the normalized multiple coefficients being below 0.75. Is that not so? Thanks, Georg On Jun 7, 2018, at 2:38 PM, Brooks, Stephen wrote: Our condition is basically 0.1% field change, so a 0.5% change in this one block would produce that at the edge. However, we don't necessarily want to degrade the magnets to the margin of that criterion (we aim for better if possible) and the estimate of damage rate has an exponential in it, so it has a big proportionate error bar. That's why I chose the 1000Gy accumulated dose level, giving 0.02% change in field, as a safe limit. -Stephen From: Georg Heinz Hoffstaetter Sent: 07 June 2018 14:33:09 To: Brooks, Stephen Cc: Georg Heinz Hoffstaetter; James Arthur Crittenden; Wei Yuan Lou; Berg, J Scott; Trbojevic, Dejan Subject: Re: Sensitivity to demagnetization Hi Stephen, this is extremely helpful. What I can’t see quickly from this is by how much the magnetization of this one block can change until the magnet would not pas our acceptance criterion. Do you have that number? Thanks a lot, Georg On Jun 7, 2018, at 1:47 PM, Brooks, Stephen wrote: I tried a worst case for a single block being 1% weak, so took a lopsided BD and made one of the largest blocks near the midplane 1% weaker. The result is about a 0.2% field change and 0.5% gradient change at the worst point (the one nearest the block). Although we don't have beam there as it turns out. The worst harmonic is 7.4 units of sextupole (out of 10000, so compare 10000*1%=100 and 100/16 = 6.25). Anyway, this is what I said: overall magnet parameters change by 1%/16. Worst-case points and local nonlinearities change by less than, but of the same order as, the 1% error put in. -Stephen From: Georg Heinz Hoffstaetter Sent: 07 June 2018 11:55:54 To: Brooks, Stephen Cc: Georg Heinz Hoffstaetter; James Arthur Crittenden; Wei Yuan Lou; Berg, J Scott; Trbojevic, Dejan Subject: Re: Sensitivity to demagnetization Hi Stephen, This is unexpected and rather interesting. I am sure you presented this before and I forgot or missed it. I will try to dial into the 11am meeting today. Would you be able to show the data again. If it is too short notice we could try again in two weeks when I will be back at Cornell. Thanks, Georg On Jun 7, 2018 10:47 AM, "Brooks, Stephen" wrote: Changing the individual block strengths is something I did in the error studies. It's not really the relevant thing to look at because absolute magnet strength (or at least strength relative to the other magnets) also matters. The dependence is pretty trivial: if one of the 16 blocks got reduced in magnetisation by 1%, the average field decreases by 1/16 %, there is some nonlinearity introduced but it's below the 1% level. So I kept magnetisation loss below about 0.02% in my study, which ensures whatever the geometry of magnetisation loss, the field is still OK. -Stephen From: Georg Heinz Hoffstaetter Sent: 06 June 2018 17:41:40 To: Brooks, Stephen Cc: Georg Heinz Hoffstaetter; James Arthur Crittenden; Wei Yuan Lou; Berg, J Scott; Trbojevic, Dejan Subject: Re: Sensitivity to demagnetization Dear Stephen, unfortunately I missed you, it was a full day. I don’t see that your presentation is answering my question directly. Is there a simulation where you change one block by x% and you then see how strongly the multipole components get exited. Has this been done? Thanks a lot, Georg On Jun 6, 2018, at 11:22 AM, Brooks, Stephen wrote: OK. I'm here (BNL) this afternoon and will be in my office from 2pm. -Stephen From: Georg Heinz Hoffstaetter Sent: 06 June 2018 11:19:52 To: Brooks, Stephen Cc: Georg Heinz Hoffstaetter; James Arthur Crittenden; Wei Yuan Lou; Berg, J Scott Subject: Re: Sensitivity to demagnetization Hi Stephen, that’s great and looks rather complete. Are you here, can we talk about this some time this afternoon? Thanks, Georg On Jun 6, 2018, at 10:42 AM, Brooks, Stephen wrote: -Stephen From: Georg Heinz Hoffstaetter Sent: 06 June 2018 10:30:21 To: Brooks, Stephen Cc: Georg Heinz Hoffstaetter; James Arthur Crittenden; Wei Yuan Lou; Berg, J Scott Subject: Re: Sensitivity to demagnetization Cool, can you send it, please, along with the study that supports this. Thanks, Georg On Jun 6, 2018, at 10:13 AM, Brooks, Stephen wrote: This is in the baseline parameters spreadsheet, tab "1.5 Halbach", line 25. -Stephen From: Georg Heinz Hoffstaetter Sent: 06 June 2018 10:08:44 To: James Arthur Crittenden Cc: Wei Yuan Lou; Berg, J Scott; Brooks, Stephen Subject: Sensitivity to demagnetization Hi Jim, Ritchie, Julia, and I were at Germantown DOE-NP last week and one important question came up to which I should have known the answer, but did not. Here the question: How much radiation damage can be tolerated in an FFA magnet? More precisely, I think we should take a perfect FFA magnet and see how much the magnetization can be reduced in each PM block separately until the magnet would not longer pass the acceptance criterion. I am cc.ing William because of his involvement in the acceptance criteria, as well as Stephen and Scott for obvious reasons. James, Is that something you can do? And how long do you think it would take? Thanks, Georg