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Registered Member #58215
Joined: Wed Dec 30 2015, 11:27AM
Location: Boise, Idaho
Posts: 65
Lying in bed last night, a few ideas hit me for improving the efficiency of the starting coil of a coilgun. The same principle would work for later coils, but later coils do not suffer from the same inefficiency as the first coil. The primary concerns I tried to address were to make "switching off" the magnetic field easier, and to provide a carefully modulated rise in the field to both give the projectile time to magnetize, and so as to not increase the strength too quickly. Inertia is a nasty thing for coilguns, as the projectile doesn't accelerate nearly as quickly from rest for the same force input.
It's rather late (1 AM when I started this and 4 AM now) so I could be an a sleep-induced science high and not actually thinking or spouting anything sensible. If I know anything from reading threads on this forum, you get roasted if you say something stupid, but at least I have simulations to add?
Firstly: Question: If a magnetic field started acting on a projectile from rest, would the projectile benefit more from a gradual curve, or would the effect be identical no matter how steep the curve is? If the curve was nearly vertical, a projectile would accelerate much more quickly, but does saturation of the projectile material cause a limit for the rate of acceleration? Or is saturation just relevant to the maximum field strength at which the force on a projectile will occur at? Conceptually, a large force over a short time equals a short force over a long time if the energy imparted is the same, and also a short pulse is greater than a long pulse with regards to energy lost to heat dissipation. (another reason why later coils can be more efficient).
Below is the post I made to PhysicsForums in its entirety. I refrained from mentioning that it was for a coilgun, which might have hurt responses, but also I do not know if the forum bans such topics as many of them do, and I did not want my post deleted.
Hello, and thanks for looking at my question. For starters, this is NOT a homework question, or a question I will receive any credit for except maybe a "hey, cool". The level of difficulty is roughly a junior-year Electromagnetics class homework quesiton, I suppose?
My Question is rather open-ended. Because of the nature of the problem, I am asking for general answers to help me focus on what to simulate, I am not asking any members to simulate or do iterations by hand. If such open-ended questions are not allowed and this needs to be removed, then I apologize, I read the forum rules and saw nothing banning them.
Specifically, feedback I would like: Ideas for how to shape the field and external material to fit the design constraints. A crudely drawn paint image with materials labeled (I am using 600A of 18AWG copper wire, 1000 turns for coil simulation) for any ideas of coil/external iron shape would be great. I have some simulations done, and any analysis of those results would be helpful as well.
I am looking at non-symmetrical coil shapes in an attempt to "shape" the intensity inside the coil. A solenoid is generally symmetrical, so I will refer to it as a coil. Picture is the fastest way to describe what it is that I mean by non-symmetrical.
My desire in shaping the field is to form an intensity shape which is long on one side of the maximum and short on the other side. Graphs work best to show the picture here. Typical Magnetic Field inside a normal solenoid: http://imgur.com/wyeUxQY
The "Ideal" Shape for me (not realistic, just Ideal) Is for the Magnetic field to build up roughly exponentially, then drop to 0 at the exact point that the field is most intense. Because the inductor won't drop its current to 0 instantly, and ignoring any electrical "tricks" that can get it to drop extremely quickly, I am looking for a design to get me close to this: Actualy, the ideal curve would have a perfectly flat or gently curved top (a constant magnetic field being just as good as no magnetic field, and a flat spot giving a good place to flip the current off) not a sharp pointy one, but it's already been uploaded.
There is more to the problem, of course, and some other constraints might help. Most importantly, the coil will have an air gap inside, and must maximize interior field strength while minimizing the length of the coil (from entrance to exit of center hole, not wire length except for lower resistance). The coil also must minimize resistance and inductance, while providing a very specific field strength at the very center of the coil (With the desired field strength corresponding to the inner diameter, overall coil length, values for inductance and resistance, and the "length" of the field from the maximum to the edge of the coil). It cannot have a ferromagnetic core, but small may have small mounts of external iron (or other magnetic material) to guide or shield the flux. Depending on the maximum value of T I will also need to carefully regulate the slope of the graph of Field Strength vs distance from coil start to its maximum value. Fortunately, I can make simulations in FEMM and use some RLC circuit simulations to help with the work once I have a good idea from the FEMM simulation. The hard part now is thinking of what to put into the simulation.
My attempt at a solution/my current work: Some brainstorming, and some FEMM simulations of what I think such a coil would look like. I have yet to do the problem by hand as I am simply looking at generalized shapes. Coil shape: Tried an "L" shaped coil: skinny at the top, and thick at the bottom. It caused the field to drop off more quickly and to "ramp up" more slowly:
External Material: Looked at using pure iron (hopelessly rare but a very very good magnetic material): You can clearly see that this causes the field to drop off more quickly! It was a rather large slab of iron, though, and length of the coil is a primary concern, so It has yet to be seen if this would be of actual benefit, but in theory it has the desired effect. (If someone wants to see what any of this looks like in FEMM I will be more than happy to share, I just don't want to upload a ton of pictures to IMGUR for the question).
Okay, that worked, so how about MORE external Iron? or Steel? (fixed Nd magnet simulation on outside did not have any relevant effect on the magnetic field). For testing purposes to see the effects, the external material was 50% of coil length (unnacceptable length) but that did help me see what worked.
Trying different configurations of external Iron and steel: The strength of the field at the center was raised considerably, and the magnetic field wanted to drop off more quickly outside of the coil, as the flux lines are being redirected. Iron helps, but not a whole lot. Curve from Grade A carpenter's silicon steel: placed like this (4hv note: put the explanation in of where the steel and coil were for all the physicsforum guys who wouldn't know) As a side note, the steel increased the magnetic field in the center by 50% compared to 8% for pure iron. The corner of the steel closest to the "Exit" (bottom in pic) of the core was magnetized to 23T in simulation (almost 100% more!). And about 19T in center. (I realize that specific numbers here are not helpful, but the general trends and % increase are). A few other magnetic steels had the same effect. A different material called supermalloy was the best, with over a 100% increase in core field strength and a much greater field falloff curve. (Incidentally, if any physics majors need a ~30T-50T field for a few milliseconds, simulations say it is pretty dang easy to do. You could easily sustain the field too if you had liquid nitrogen cooling. All stuff available at a typical university!)
So, it seems clear that an external end cap can help "cut off" the field more quickly.
Combining the "L" shape with Grade A carpenter's silicon steel: Shape for simulation:
Simulation results through center of core:
And the most interesting portion, the Simulation results through the innermost edge of the coil and steel external piece. Also occured for the normal shaped coil, of course.
4hv note: Is this beneficial to the gun in some way? some extra force after the projectile passes through the coil, while the steel is demagnetizing? Or is it negligible considering energy wasted to magnetize the steel in the first place?
This seems pretty close to what I want. I am thinking about trying ramps rather than the "L", trying an extremely thin piece of silicon steel (coil you see is 40 mm tall, by thin I mean 1/2 -1 mm) along the inside of the coil. Do you guys think that would be a good idea? Are there any problems with these sims, that FEMM doesn't realize or that I am doing wrong? (will the external material "steal" the energy that would go to a ferromagnetic object in the core?) I'm asking this before I spend more time doing simulations. I think that I am on to something here with the combinations, I just won't know until I can build models in the lab: one of a normal solenoid, and one that I design, both with the same calculated inductance and resistance. Obviously, I would like to run simulations and think a lot before I purchase wire and high grade steel and spend a long time winding the cores.
Note: All simulations graphs show field strength from about twice the distance of coil length, through center of coil, to same distance away. 0 is the "top" shown in simulation pictures, and the maximum is the "bottom". The top is the coil "entrance" and the bottom (Where the external material is) is the "Exit"
back to 4hv post:Edit: uhh.. these pics ended up huge. Tried switching them to be links, but the links wouldn't work (appeared as links, went to error page) ended up making them small thumbnails. You can also see the normal pics (WITHOUT the 4hv extra notes, mind you) at <https://www.physicsforums.com/threads/
electromagnetics-non-symetrical-coil-with-
external-iron.851015/> if you copy paste that
Registered Member #2906
Joined: Sun Jun 06 2010, 02:20AM
Location: Dresden, Germany
Posts: 727
This is tooooooo much text
If I know anything from reading threads on this forum, you get roasted if you say something stupid
Sry
there any problems with these sims, that FEMM doesn't realize or that I am doing wrong?
Hmmh. Its the most important question i could find Short answer: you stated something about 30-40Tesla!? I am sure with all your reads in this forum you cam across the word "saturation"? There is a point in every ferromagnetic material where all magnetic domains are oriented the right way. It will then not get magnetized any more and the µr drops to 1. With iron this point is reached at ~2T. If in your simulation the iron/steel works above 2T then FEMM is not considering the real µr(B) In my experience even reaching 6-8T in a controled way is a very hard job with home electronics. Of course you can dump raw power into the coil.. but thats expressed in your words "not engineering"
Soooo to your main question: will it help the Coilgun? No. Yes. No. Maybe yes. But No. Basically every change in velocity is bad for efficiency (change in velocity is not refered to acceleration dv/dt but v_end-v_start for a certain coil). The efficiency increases as the velocity change lowers. If you reduce acceleration of the first coil you have to spend more effort in the following coils to reach the same exit velocity. I found no positive effect in distributing the burden. So your coil benefits from your stuff, the coilgun does not. If you coilgun is "the coil", then the coilgun.. well i actualy dont know the outcome. Why i dont know? Because such solution is to be avoided by all means Dont shape the magnetic field by geometry. Shape the acting force with the help of electronics! You benefit much more by good coupling between coil and projectile and you profit much more by putting effort in conductor density.
For SCR-based designs its known that external iron migt improve things. But improving a bad concept will still yield a bad concept. Let me put it this way: i know from my half-bridge-CG that when the gun is optimized, iron will not help anymore. But it also depends on your optimization goals. I optimize Ekin*Eff^2. So i weight efficiency twice as much as output power. If you are more into efficiency then you will have automatically lower currents and less saturation. With less saturation external iron might begin to work again. But i do not see any coilgun with reasonable output power that will have less than 2 Tesla.
I will not "roast" you :D but your concept. Surely.. scientificly interesting.. but from an engineering standpoint.. just No. If you use electronics you can do the same things but you can adjust everything at will. Wouldnt you prefer that?
Firstly: Question: If a magnetic field started acting on a projectile from rest, would the projectile benefit more from a gradual curve, or would the effect be identical no matter how steep the curve is?
If I make some simplifying assumptions, then no. Lets assume, that the B field does not change with time and that the iron is not saturated. Then the force on the projectile is:
F ~ dB²/dx (~ means proportional to)
The energy imparted to the projectile is
E = integral (F*dx)
along the path of the projectile. The integral then amounts to
E ~ Bfinal² -Binitial²
Binitial being the field at the beginning of its path and Bfinal at its end. So the energy gain is independent of the shape of the field. Actually the gain is zero if Binitial and Bfinal are the same. For saturated iron, that is different, but probably not to a big extent. The energy imparted depends much more on the time dependence of B. You need to make assumptions about that before you can reasonably talk about dependence on field shapes.
Registered Member #58215
Joined: Wed Dec 30 2015, 11:27AM
Location: Boise, Idaho
Posts: 65
No kidding, I was going for a ~100 word question then it blew up. The roasting makes for great reads from past discussions. If someone thinks of something stupid, just let them know it is stupid.
Regarding the "30-40T" I did not mean for use in a coilgun! that was just an aside. You can concentrate magnetic fields really, really well with the use of a "guide" material, as I learned last night while doing a lot of simulations. It was just an interesting fact. The simulation gave me a 19.7 T field in the center as maximum, with steel end and side caps, and a very high current/number of turns. That is just the peak field that would occur if everything went according to the simulation for a very brief time. The realistic field inside would be 10-12T at peak for what I was simulating These are just sims. I have not yet started designing the actual gun, but rather thinking about each of the pieces briefly before I design a basic platform on which to test with.
If in your simulation the iron/steel works above 2T then FEMM is not considering the real µr(B)
I used their default material property values, I might need to define a custom B-H curve for the material. None of the simulations took into account a projectile traveling through the center, I have yet to do that (I just started FEMM yesterday after all).
Soooo to your main question: will it help the Coilgun? No. Yes. No. Maybe yes. But No. Basically every change in velocity is bad for efficiency (change in velocity is not refered to acceleration dv/dt but v_end-v_start for a certain coil). The efficiency increases as the velocity change lowers. If you reduce acceleration of the first coil you have to spend more effort in the following coils to reach the same exit velocity. I found no positive effect in distributing the burden.
Is the first coil not rather unique? For instance, if using external Iron- from my simulations, the field strength inside will be higher (letting you have smaller L and R values) with the iron. BUT, you don't want to completely close off the coil, because you want the magnetic field to "reach" further to grab the projectile from outside the coil, not moving. This is a primary example of using the geometry to help! Specifically, that is also not something that the electronics can help with- only geometry. When it comes to shutting off the field, I have no experience with it yet, but if simple geometry changes can be made to assist the electronics, even if the gain in efficiency or the gain in KE is small, it is worth looking at (even if it just for fun- I am not trying to build a coilgun to sell, I am enjoying this)
So your coil benefits from your stuff, the coilgun does not. If you coilgun is "the coil", then the coilgun.. well i actualy dont know the outcome. Why i dont know? Because such solution is to be avoided by all means Dont shape the magnetic field by geometry. Shape the acting force with the help of electronics! You benefit much more by good coupling between coil and projectile and you profit much more by putting effort in conductor density.
by conductor density you are referring to the square Aluminum wire you are ordering for your project?
For SCR-based designs its known that external iron migt improve things. But improving a bad concept will still yield a bad concept. Let me put it this way: i know from my half-bridge-CG that when the gun is optimized, iron will not help anymore.
I suppose that once I have an optimized gun and not a pile of electronic parts, I will see? I will take this advice and information, of course, but I don't see how the iron could help greatly for one switch and be insignificant for another (I am guessing that your field does not need the "boost" from the Iron? but if that is the case you could make the inductor smaller, and add iron? I will see when I do testing, eventually!)
But it also depends on your optimization goals. I optimize Ekin*Eff^2. So i weight efficiency twice as much as output power. If you are more into efficiency then you will have automatically lower currents and less saturation. With less saturation external iron might begin to work again. But i do not see any coilgun with reasonable output power that will have less than 2 Tesla.
I will decide on my design constraints when I am done fiddle-dinking around with the components and start the real design. Have to make constraints to guide the project. Why weight efficiency twice as much as kinetic energy? You are counting in recouperated energy for the efficiency as well. That gives more weight to the efficiency than simply two times. If you don't count recouperated energy into the design, then the "efficiency" is only the amount of energy going into the projectile and they end up the same, I suppose (more efficiency is more kinetic energy in that case). If I had to choose between 30% efficiency, with 10% of that being from recouperated energy (with regard to the max stored energy) and 25% efficiency, but all of it going to the projectile and no recouperated, of course I would pick the second option. The batteries and charging circuitry is much easier to design to function well than it is to squeeze more kinetic energy out. Efficiency for recouperated energy helps with the rate of fire and the time the gun can be used before a recharge, but again..those seem like the easier things.
I will not "roast" you :D but your concept. Surely.. scientificly interesting.. but from an engineering standpoint.. just No. If you use electronics you can do the same things but you can adjust everything at will. Wouldnt you prefer that?
Everyone needs to be roasted. I think I can see some value in looking into changing coil shapes slightly, and using iron to focus the magnetic field. I also find it quite interesting. (A lot of small changes that help in small amounts is a big change). I will at least do some testing once I have a platform to test built before throwing out the idea.
Thanks for the reply
Uspring: Thanks for the reply!
If I make some simplifying assumptions, then no. Lets assume, that the B field does not change with time and that the iron is not saturated. Then the force on the projectile is:
Binitial being the field at the beginning of its path and Bfinal at its end. So the energy gain is independent of the shape of the field. Actually the gain is zero if Binitial and Bfinal are the same. For saturated iron, that is different, but probably not to a big extent. The energy imparted depends much more on the time dependence of B. You need to make assumptions about that before you can reasonably talk about dependence on field shapes.
My physics and engineering textbooks rely on simple assumptions and approximations. If I know anything, it's that the approximations exist for a good reason, but at the end it is still an approximation for most things. The same for assumptions- for some problems, they work perfectly, and for others, it just makes it simple. It's hard to tell when they will be very close and when they will simply show the trend. "For saturated iron, that is different, but probably not to a big extent" <- I find this very likely, but even a little help to efficiency will help.
You are right. I need to know what sort of RLC circuit I will have for the gun, projectile and coil size, etc. before I can see if it helps and make any assumptions I need to make, for that specific design. I just thought it would be beneficial to try to analyze if such things were worth any time or thought into at all. Now I wonder if I can find any papers on how iron responds when it is near-saturated or saturated?
(This question also has to do with the optimal initial projectile placement, and how to shape the magnetic field/use electronics effectively. I plan on trying to work on that once I have a platform to test with up).
Registered Member #2906
Joined: Sun Jun 06 2010, 02:20AM
Location: Dresden, Germany
Posts: 727
Soooohh much text agaaaaain
You can concentrate magnetic fields really, really well with the use of a "guide" material, as I learned last night while doing a lot of simulations. [....] The realistic field inside would be 10-12T at peak for what I was simulating
NooooOOOOOoooHHHHhhhh! <- Roasting Understand the problem with saturations: There is simply no material that is a "guide" at those field strengths. Above 2T every material will just be like "not there" and therefor there is no guidance anymore. This is an important switch that has to click in your head. Just repeat saying it "there is no magnetic guidance above 2T" like Bart Simpson.
but I don't see how the iron could help greatly for one switch and be insignificant for another
Because of saturation. In a bad coilgun you are just happy if anything actually moves. In an optimized coilgun you will start trading off efficiency (which happens basically by allowing saturation) for output energy just because you can. As soon as there is saturation happening the external iron is "not there". Its just useless mass. Aaaaah and the eddy currents. dont forget them. What the iron acutally does is to improve the L/R-Time constant. You get more Inductance for the same wire length. But only if the irong is magnetically active. It helps with SCR-Based design because they are so bad that every improvement is noticable. With a different concept that little improvement will vansih in measurement uncertainty. Then what?
by conductor density you are referring to the square Aluminum wire you are ordering for your project?
No thats actually an act of desperation due to the extreme weight of copper What i mean is: wind the best coils you can to have a good L/R-Time constant. Having complicated coil formers and bad winding due to some complicated coil design will actually work against you at some point. L/R is the most important thing in a half-bridge design.
You are counting in recouperated energy for the efficiency as well. That gives more weight to the efficiency than simply two times.
No If the acceleration is done i recycle the left over energy in the coil. This is a mechanism to incease efficiency but it does not give "weight" to it when speaking of a "figure of merit"-Optimization. You can apply a FOM of "Ekin*Eff^2" or "Ekin*Eff^3" or "Ekin^2*Eff" to every concept and find the maximum [best implementation according to your goals]. The underlying system will then be optimized no matter how its constructed. Thats the whole concept of a "firgure of merit" (FOM): you can directly compare concepts by objective means.
In the mean time i think that Uspring has a major point -> . However the conclusion
E ~ Bfinal² -Binitial²
i cant follow. since you cant do that with differentiation and integrals. A coil starts at B=0 and ends at B=0 when shut off after a while. So E is allways 0. But anyway the idea is the right one.
Registered Member #58215
Joined: Wed Dec 30 2015, 11:27AM
Location: Boise, Idaho
Posts: 65
yes, sorry, I prefer to reply to things in length so that a full discussion can happen.
Understand the problem with saturations: There is simply no material that is a "guide" at those field strengths
10-12T referred to the Field strength inside of the coil, which is perfectly reachable. After reaching saturation, the permeability of the material drops to 1, which is the same as air, so a field would no longer want to be guided, yes. But with some geometry, what If I have miltiple cones at saturation "transmitting" tthe flux lines all into one small area? I can't find any tests online with fields smaller than milliTesla the effect would get a little boost again if a diamagnetic material was used around the material instead of air. I don't know what the realistic maximum would be for such a concentrator, but it could easily exceed the 2T saturation point of the material.
What the iron acutally does is to improve the L/R-Time constant. You get more Inductance for the same wire length. But only if the irong is magnetically active.
This is what I was thinking the external iron would be useful for, is the L/R constant not worth the weight of the iron (for a portable design like yours) to improve? I think it would be- even very thin (a few millimeters) high silicon steel helps a field quite a bit- lets you use shorter and fatter coils so you can fit more on the barrel. Maximizing the number of coils on the barrel is a key point of an effective portable design, is it not?
No thats actually an act of desperation due to the extreme weight of copper
Have you wound the coils out of aluminum yet? How do they stack up? The Thermal conductivity of aluminum is half that of copper, if heating was already an issue.
Having complicated coil formers and bad winding due to some complicated coil design will actually work against you at some point. L/R is the most important thing in a half-bridge design.
"Keep it simple, Stupid" is right.
About the FOM: there are other factors, such as weight of the device, size of the capacitor bank, and such to consider. If your design has 1000J in the bank and when it fires, it ends at 100J from recouperation, 900J goes into waste heat and kinetic energy. If the same cap bank ended at 20J and 980J into waste heat and kinetic energy, waste heat will be higher lf course, but kinetic energy was even 2J higher, would you not prefer that? (If it is not a rapid-fire design we are discussing where recouperated energy greatly benefits fire rate)
Think about what Uspring said like a coil with a constant current. A projectile will accelerate from one side, come to a stop, then go the opposite direction. It will oscillate endlessly. It has kinetic energy at a maximum when it goes through the center of a coil, but the Net energy is 0 because the projectile moves in the opposite direction later with just as much energy. It is a closed-loop integral with no "potential" change, so the energy is 0. (Bf = Bi) this comes directly from what uspring showed. If you shut off the current when the projectile is at the peak, then Bf^2-Bi^2 does not equal 0... It equals the center of the coil Magnetic field maximum, and the projectile will leave with energy. So B does not end at 0 for the energy it transmits to the projectile I think you knew that and just didn't follow usprings ~math. I wrote that anyways because it is a nice refresher for class, haha.
i cant follow. since you cant do that with differentiation and integrals.
Its an integral with respect to x of the derivative of B² with respect to x. Where did I go wrong?
A coil starts at B=0 and ends at B=0 when shut off after a while. So E is allways 0.
It's a bit of an academic question, since, as you point out, the net energy gain is 0. The energy gain crucially depends on the turn off of the field during projectile traversal. Then it begins to make sense to discuss field shapes. What shape is best hinges on the time dependence of the field.
Registered Member #58215
Joined: Wed Dec 30 2015, 11:27AM
Location: Boise, Idaho
Posts: 65
@signification Thanks for that, I just checked it out. The coils weren't too similar, but the idea of designing the magnetic field to be a suitable shape was. A good read.
Registered Member #2906
Joined: Sun Jun 06 2010, 02:20AM
Location: Dresden, Germany
Posts: 727
Sry Uspring, maybe its just me beeing a human showing his most inherent characteristic: i didnt understand it, so i deny it And honestly i still dont understand it completely (while i am still getting the point). The problem is that B is a function of Space, and current and therefore time and projectile position. I cant break that down to one single line in a heartbeat.
When talking about efficiency i never ever would consider to start out on B. I allways acted upon the allready integrated force on the Projectile. That force is then abstract enough to eliminate enough variables. It just comes down to F=F_0(I_0, x(t))*(I(t)/I_0)^2 with x beeing the projectile position and I0 beeing the constant current with which i determined F_0(x). I then know that P_loss ~ I^2 and then i can calculate, given the right time-function of the current I, the efficiency and with that i can optimize my Current-Waveform, but never B itself. B(x,y,z,x_projectile, I(t)) could be a viable alternative, but to be honest... i can accept the fact that my last layer of wire should only be half the coil length either on the front or back-side of the coil, but i would not think about changing the coil format extensively. Its a manufacturing-boundary i simply wouldnt cross. But thats me, and me alone having that particular restriction. So... dont bother Still having written this i think its more beneficial if you try to shape the F_0(I_0, x) - to a waveform thats easily aproximated by a typical inductor current. Of couse this shapes B too.. but the process is more guided if you rely on F instead of B.
Have you wound the coils out of aluminum yet? How do they stack up? The Thermal conductivity of aluminum is half that of copper, if heating was already an issue.
No aluminium is hard to get in small quantities. Currently i only know how my models change if i use AL but nothing more and i could live with the predictions. Dont even start to think about Aluminium (which btw most heatsinks are made out of) heat management. If the dissipated energy in a coil is high enough to raise the temperature noticable then you did it wrong The major risk at this point is a thermal runaway of a hotspot.
Concerning the FOM: maybe there is a missunderstanding. I think i get where you are pointing at. Maybe its my fault not to be more precice..... Ekin*Eff^2 is the FOM to which i optimized my switching for the coils <- and only that! The whole conept however is not really influenced by that except the estimation of maximum current through my swithces and the reduced cap-size i need due to the prioritized Efficiency. The cap-size has direct implications on weight and volume of the gun and is to be considered a fact of life in the moment. The same is with the switching-elements since thats a huge price factor. First and foremost i have to make sure that electrically i can reach my goals (like 100J) and then be happy about that its actually quite small too Its just... when you finally have something working (either in simulation or real life) thats so flexible that you can optimize it at will you need to invent a FOM which repesents your _personal_ goals. It does not mean that until then you have everything built with that FOM in mind. But it might mean that during a redesign you can optimize your gun having the experience in mind which you gained using that FOM. I found that Ekin*Eff^2 leaves _ME_ with reasonable output power while having a quite small cap bank. I also tried to optimize for otehr FOMs but the predictions werent so nice for my design then. In conrast to that it also means that i acutally need more stages because i push less energy per stage - in the end someone else might have different priorities... but for me adding stages.. no problem.
"Keep it simple, Stupid" is right.
Yes and No. It depends on what you try to optimize. Changing coil geometry to a complicated shape might yield not much (even if it yields something) compared to the gained complexity. Its what i would call "a bad compromise". Increasing complexity like switching from SCR to IGBTs is however a worty step. Why? The gained complexity is justified by the gained properties. You dont need to form the B-Field anymore.. you simply form the current waveform yielding the more/same improvement and end up even more flexible. However this is a completely subjetive thing! So if you have different opinion: totally fine.
I realize that i should not try to stop such research because every gained knowledge is good, however i like to point out that you should expect not much practical use. But who knows. maybe i am completely wrong. That would be awesome!
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"Shaping" Magnetic field to be more suitable for coilgun
Short answer: you stated something about 30-40Tesla!? I am sure with all your reads in this forum you cam across the word "saturation"? 
There is a point in every ferromagnetic material where all magnetic domains are oriented the right way. It will then not get magnetized any more and the µr drops to 1. With iron this point is reached at ~2T. If in your simulation the iron/steel works above 2T then FEMM is not considering the real µr(B)
What i mean is: wind the best coils you can to have a good L/R-Time constant. Having complicated coil formers and bad winding due to some complicated coil design will actually work against you at some point. L/R is the most important thing in a half-bridge design.
the effect would get a little boost again if a diamagnetic material was used around the material instead of air. I don't know what the realistic maximum would be for such a concentrator, but it could easily exceed the 2T saturation point of the material.