Design of a Helmholtz coil pair
Jeffry T Urban
and construction of a Helmholtz coil pair, or who could point me to
appropriate references (books/journals, or even knowledgeable people).
(For the un-initiated, a Helmholtz pair is a pair of two (usually)
circularly-wound wire coils aligned axially with current running through
them in the same direction; they are spaced a mean distance from each
other equal to the mean radius of the coils. These coils are used for
generating relatively uniform magnetic fields.) If you are reading this
and are not interested in helping, I urge you to skip the rest of this
message, since I'm going to include some technical information that will
probably bore you to death. However, if you are interested in helping,
please read through the message even if you don't know much about the
subject, as there might be some small matter with which you could help.
I request that replies be directed to me via e-mail, since I'm not sure
how often I'll get a chance to check the net groups.
I am an undergraduate chemistry major working in a university
chemistry lab. I have to design a coil pair that will be placed inside
a spectrophotometer so that I may measure the effects of a magnetic
field on a particular chemical reaction. I have a target field
strength, and obviously since the coils will be placed inside a cavity
in the spectrophotometer, I have rather limiting size requirements.
Being just a lowly undergraduate chemistry major, I don't know much
about coil design; I've done plenty of library research, and while I've
found extensive material on the magnetic field generated by a Helmholtz
pair, I've found relatively little on coil design, and even less on coil
construction. I'm going to give some technical information regarding
the coils I need:
MAGNETIC FIELD: I need a maximum field of strength 500 - 1000
gauss (0.05 - 0.1 tesla). I'm not sure how uniform the field has to be
(the spectrophotometer sample chamber in which I need to generate the
field is 2x2x4 cm), but I think that's going to be the last of my
concerns.
COIL SIZE: I'm working in a rather small space. The coils should
have outer radii (read radii, not diameters) of no more than about 7.5
centimeters to fit in the cavity. They're probably not going to be able
to be placed closer than 3.5 cm between their inner surfaces (this also
implies using the Helmholtz condition of the average distance between
the coils being equal to the average radii of the coils, that the
average radii of the coils ((inner radius + outer radius) / 2) is going
to be a minimum of 3.5 cm (and that assumes that the coils are
negligably thick)).
WIRE: It looks like I will probably use copper wire. I'm not sure
of what type or what gauge, however. Of course, varying the gauge is
going to vary the resistance of the coils (and consequently the amount
of current I can put through the coils with a given voltage, which will
determine the magnetic field strength). The gauge will also help
determine the size of the coils, and probably the number of turns of
wire per coil. A very important bit of information I need to know is
how to wind such coils.
POWER SUPPLY: I'd like to have some suggestions as to what type of
power supply to use if I want to vary the magnetic field. I don't care
much about the voltage right now, as long as it's sufficient to do the
job and not too much so that it would massive overheating of the coils.
WIRING: Does anyone know how to wire such a device? It doesn't
look to challenging, but I hardly know anything about electronics, so
it's better safe than sorry. A rough circuit diagram would be helpful.
I've also considered wiring the two coils separately to different power
sources so that I could decrease resistance. They're usually wired in
series. The problem with two sources is that checking to see if both
coils are generating the same magnitude of magnetic field (well, the
other problem is that two power sources is inconvenient). It would be
easy to tell if the coils were generating the same magnetic field by
switching the direction of current in one coil so that the two magnetic
fields oppose each other, and then fiddling with the voltage in that
coil until the field is zero at the middle of the coils along their axes
(then the magnitude of the fields generated by each coil would have to
be equal), and then all I'd have to do is switch the direction of the
current in that coil back again and they'd be adjusted.
POWER DISSIPATION: I'd really like to keep the coils from
generating very much heat, because if I have to include a cooling
system, not only is that inconvenient, but I have to worry about space
requirements. I'm not sure how long I'd have to keep the coils on, but
I could find out. (Probably not *too* long since I'm doing fast
kinetics experiments, but then again I wouldn't want to wait forever
between kinetic runs for the coils to cool back down.)
THE PROBLEM: *** How can I generate my desired magnetic field with
a minimum of heating and fit the coils in the desired space, by varying
the size of the coils (inner and outer radii, thickness, etc.), the
gauge of wire, the number of turns of wire in each coil, and the power
supply voltage? ***
USEFUL INFORMATION: The equation for the magnetic field generated
at the center of a Helmholtz pair along their axes is:
B = 0.7155 * u0 * N * I / r,
where B is the magntitude of the magnetic field, u0 is mu naught (4*pi x
10^-7 in mks), N is the number of turns in each coil, I is the current
in the coils, and r is the average radius of each coil. This equation
is for the net field generated by both coils, which should be exactly
equivalent in size, spacing, and number of turns of wire. The
resistance of two coils wired in series is:
R = 2 coils * N turns/coil * (2*pi*r) * rho,
R = 4*pi*N*r*rho,
where R is the total resistance, N is the number of turns per coil,
2*pi*r is the length of wire per coil, and rho is the resistance of the
wire per unit length (which depends on wire composition (i.e., copper)
and gauge). R and I can be related through Ohm's law, V = IR. Power
dissipated (assuming total dissipation as heat) is P = VI = IR^2.
ALTERNATE METHODS: If Helmholtz coils are impracticable for my
needs, what else can I use that will work, and how can I
design/construct the system? I've got a very tentative theoterical
configuration which will dissipate about 50 W for the two coils (more
than I'd like), but it uses a rather large diameter of wire, and I don't
think I'll be able to make the coils a sufficent thickness.
Well, that's about all I can think of right now. If you are
reading this and know anything about any of the topics I've covered or
know someone who does or where I could look this stuff up, please write
me. If you need more information, ask me and I could probably get it.
Address replies to:
If you feel the urge to phone, it's (412) 268-5671 (U.S.A.) during
weekday work hours in Eastern Daylight time. Ask for Jeff.
Thanks very much in advance,
--Jeff Urban
Douglas P. McNutt
<ju...@andrew.cmu.edu> wrote:
> I'm looking for people who could give me information on the design
>and construction of a Helmholtz coil pair
It looks as though you have done your homework.
My gut feeling (I have built a few Helmholtz coils) is that you are going to
have a SERIOUS heat problem unless you pulse the coil. AND, if you pulse the
coil you are going to have to worry about its inductance and the shape of
the current curve with time. You'll be looking for something more like a TV
horizontal deflection circuit than a power supply.
Most H coils are used for cancellation of the earth's DC field at 0.5 gauss.
Adding some iron to the design to take advantage of some mu can make life
easier up to 5000 gauss.
From the USA. The only socialist country that refuses to admit it.
SCOTT I CHASE
> I'm looking for people who could give me information on the design
I second the comment of the previous poster who said that it looks like
you've done your homework already. I just have a few comments which
you might find helpful. I don't have any books to recommend, just
some experience gleaned over the years, having built one pair of coils,
and used several others.
Helmholtz coils are the way to go. They are cheap and easy to make, and
easy to operate as well.
Before getting to the details, I have one general piece of advice:
build a prototype as quickly as possible after you have settled on
basic design parameters. Don't try to make it fancy. Just throw
it together and test it. You will figure out quickly what the
problems are, if any, and how best to spend your effort on the
final product, if the prototype itself isn't good enough to do the
job.
Now to some specifics:
You didn't say how critical uniform field is. The minimum size of your
coil may be set by the maximum dB/B you are willing to tolerate over
your sample chamber. I don't recall the formula for how rapidly the field
varies with R, but you can be sure that it is slower for larger coils.
> WIRE: It looks like I will probably use copper wire. I'm not sure
>of what type or what gauge, however...
>... how to wind such coils.
The answer to "how to wind the coils" depends, in general, upon how
critical it is that you maintain a smooth, known, field. If the field
must be uniform within some tolerance which is near the limit of the
design performance of the coil, then this will require care. But it
is much better to overdesign the coil, and then not worry about imperfections
introduced in the manufacture.
To wind the coil, just do the obvious job by hand. Try to obtain the
longest pieces of wire possible, as the largest imperfections will likely
come from the splices. (I know of a scientist who pulled an ancient
telegraph repairman out of retirement to teach her grad students how to
splice wire for a critical application!)
The easiest thing to do is to not sweat the details, but then to have
a magnetometer handy to survey the device at operating current, so that
you are working with a well-characterized tool, even if it is not perfect.
I don't know if you have access to a machine shop. But if you do, make
yourself a core upon which to wind the wire which will make them easy
to handle when they are operating and are too hot to touch directly.
I have coils which are wound on aluminum cores which look like this, in
cross section. (This is a central hollow cylinder with flanges):
| |
| |
-----
-----
| |
| |
The wire is wound in the channel, and the flanges are wide enough to there
is something to grab hold of other than wire. Drill a small hole near the
inner diameter of one of the two flanges so that you can feed out the starting
end of the wire.
If you have the machine shop, you can also build a rig which will let you
use a lathe as a winding tool, if you really must have pretty uniform
windings.
> POWER SUPPLY: I'd like to have some suggestions as to what type of
>power supply to use if I want to vary the magnetic field. I don't care
>much about the voltage right now, as long as it's sufficient to do the
>job and not too much so that it would massive overheating of the coils.
What you want do to is to buy (if you have some cash) a variable current
source. Design the coil, if possible, to require no more than a few amps.
5 amp.max. variable-current sources are inexpensive, easy to use, and can
even be computer-controllable if you are into automation or remote control.
> WIRING: Does anyone know how to wire such a device? It doesn't
>look to challenging, but I hardly know anything about electronics, so
>it's better safe than sorry. A rough circuit diagram would be helpful.
I recommend that you don't burn a lot of time and energy on designing
your own control electronics. Buy a current source and just plug your
coils in, in series. No problem. Designing a current source of your
own is possible. I bet that you can find a schematic in Horowitz and
Hill's _Art of Electronics_. But this is a project in itself. You
want to do chemistry, not electrical engineering. Stick to off-the-shelf
stuff. And don't expect it to cost you less to build it yourself. It
may seem so when you price the components before you start the project.
But in the end, I doubt you can save much money over an inexpensive
store-bought current source.
>I've also considered wiring the two coils separately to different power
>sources so that I could decrease resistance. They're usually wired in
>series. The problem with two sources is that checking to see if both
>coils are generating the same magnitude of magnetic field (well, the
>other problem is that two power sources is inconvenient).
That's right. Stick to one source. It's simpler and more reliable.
There are probably no pratical reasons to do otherwise, unless you
already have two current sources available to you free, but which
can't individually handle the load.
> POWER DISSIPATION: I'd really like to keep the coils from
>generating very much heat...
Sorry, there is no easy way around this one. 1KGauss coils will get hot.
Remember also that the field will be temperature dependent. Hot coils
have more resistance than cold coils. So you need to control for
temperature or continuoiusly calibrate the coils during or between
experimental runs.
Good luck.
-Scott
-------------------- Physics is not a religion. If
Scott I. Chase it were, we'd have a much easier
SIC...@CSA2.LBL.GOV time raising money. -Leon Lederman
John Ackerman
>> I'm looking for people who could give me information on the design
>>and construction of a Helmholtz coil pair...
>Helmholtz coils are the way to go. They are cheap and easy to make, and
>easy to operate as well.
>Before getting to the details, I have one general piece of advice:
>build a prototype as quickly as possible after you have settled on
>basic design parameters. Don't try to make it fancy. Just throw
>it together and test it. You will figure out quickly what the
>problems are, if any, and how best to spend your effort on the
>final product, if the prototype itself isn't good enough to do the
>job.
A wire table and a few quick calculations will tell this person whether or
not a Helmholtz coil will do the job here. Unless he just wants to acquire
coil-winding expertise, there's no point in building it if it won't work.
Richard Karlquist
Jeffry T Urban <ju...@andrew.cmu.edu> wrote:
> I'm looking for people who could give me information on the design
>and construction of a Helmholtz coil pair, or who could point me to
>appropriate references (books/journals, or even knowledgeable people).
>(For the un-initiated, a Helmholtz pair is a pair of two (usually)
We use these all the time here at HP. You wind each coil as a
"zero length" coil, that is, you bundle all the turns together in
a bunch like multiconductor cable. You space the two coils about
a half diameter apart. Wire the coils in series so you get the
same current. Nothing critical about # of turns or wire size, it
just affects the resistance your power supply has to drive.
>
> MAGNETIC FIELD: I need a maximum field of strength 500 - 1000
>gauss (0.05 - 0.1 tesla). I'm not sure how uniform the field has to be
Here's the big problem. You can't generate those kind of field
strengths without iron pole pieces to focus the flux. We use our
Helmholz coils at 10 gauss or less. So what you really need to do
is build a iron magnetic structure and then excite it with a coil wound
around it. There are many references that describe how to get the
most uniform field between the pole pieces; you should read the
literature.
>me. If you need more information, ask me and I could probably get it.
>Address replies to:
>
> ju...@andrew.cmu.edu
>
>If you feel the urge to phone, it's (412) 268-5671 (U.S.A.) during
>weekday work hours in Eastern Daylight time. Ask for Jeff.
>
> --Jeff Urban
Rick Karlquist
rka...@scd.hp.com
Samir Mittal
Richard Karlquist <rka...@scd.hp.com> wrote:
>In article <whxRaqe00...@andrew.cmu.edu>,
>Jeffry T Urban <ju...@andrew.cmu.edu> wrote:
>> I'm looking for people who could give me information on the design
>>and construction of a Helmholtz coil pair, or who could point me to
>>appropriate references (books/journals, or even knowledgeable people).
>>(For the un-initiated, a Helmholtz pair is a pair of two (usually)
>
>strengths without iron pole pieces to focus the flux. We use our
>Helmholz coils at 10 gauss or less. So what you really need to do
>is build a iron magnetic structure and then excite it with a coil wound
>around it. There are many references that describe how to get the
>most uniform field between the pole pieces; you should read the
>literature.
>
Hi:
Upon the comment to read relevant literature, could someone
provide pointers to good books on design of such coils
and other associated eletromagnetic structures. I am not
in the area but i need to design a magnetic system, so any
such reference list will be very highly appreciated.
thank you.
samir mittal
geh...@pib1.physik.uni-bonn.de
> I'm looking for people who could give me information on the design
>and construction of a Helmholtz coil pair, or who could point me to
> MAGNETIC FIELD: I need a maximum field of strength 500 - 1000
>gauss (0.05 - 0.1 tesla). I'm not sure how uniform the field has to be
>(the spectrophotometer sample chamber in which I need to generate the
>field is 2x2x4 cm), but I think that's going to be the last of my
>concerns.
Tough problem...
>
> COIL SIZE: I'm working in a rather small space. The coils should
>have outer radii (read radii, not diameters) of no more than about 7.5
>centimeters to fit in the cavity. They're probably not going to be able
>to be placed closer than 3.5 cm between their inner surfaces (this also
>implies using the Helmholtz condition of the average distance between
>the coils being equal to the average radii of the coils, that the
>average radii of the coils ((inner radius + outer radius) / 2) is going
>to be a minimum of 3.5 cm (and that assumes that the coils are
>negligably thick)).
Ok after a quick run of a field calcualtion program here are the results
of the Bonn jury:
With coils of this dimensions you could obtain a field of 0.1 T:
inner radius: 3.5 cm
outer " 7.5 cm
gap between the coils: 5cm
width of one coil 5 cm
The current would be approx 6.5 Amp assuming a wire with 1 mm diameter
and a overall diameter of the wire (with insulation) of 1.1 mm
fine but...
>
> POWER DISSIPATION: I'd really like to keep the coils from
>generating very much heat, because if I have to include a cooling
>system, not only is that inconvenient, but I have to worry about space
>requirements. I'm not sure how long I'd have to keep the coils on, but
>I could find out. (Probably not *too* long since I'm doing fast
>kinetics experiments, but then again I wouldn't want to wait forever
>between kinetic runs for the coils to cool back down.)
would be more than 400 Watts !!! (looking at your comment below this is
not acceptable) The main problem is that you cannot
reduce this power by choosing another wire... If you use a greater
diameter if the wire. You will get less windings per coil and you'll need
more current. Anything wil remain the same :(
>
> THE PROBLEM: *** How can I generate my desired magnetic field with
>a minimum of heating and fit the coils in the desired space, by varying
>the size of the coils (inner and outer radii, thickness, etc.), the
>gauge of wire, the number of turns of wire in each coil, and the power
>supply voltage? ***
>
I think some type of setup with iron may help, but I cannot give you any
advice here.
Maybe some sort of superconducting setup ???
> ALTERNATE METHODS: If Helmholtz coils are impracticable for my
>needs, what else can I use that will work, and how can I
>design/construct the system? I've got a very tentative theoterical
>configuration which will dissipate about 50 W for the two coils (more
>than I'd like), but it uses a rather large diameter of wire, and I don't
>think I'll be able to make the coils a sufficent thickness.
>
> Well, that's about all I can think of right now. If you are
>reading this and know anything about any of the topics I've covered or
>know someone who does or where I could look this stuff up, please write
>me. If you need more information, ask me and I could probably get it.
>Address replies to:
>
> ju...@andrew.cmu.edu
>
Maybe you should read B.Montgomery:'Solenoid Magnet Design'
Wiley-Interscience 1969 to get some more hints...
Rainer Gehring
***********************************************************************
*Rainer Gehring, Physikalisches Institut der Uni Bonn *
* Nussallee 12, 53115 Bonn, Germany *
*Internet: geh...@pib1.physik.uni-bonn.de *
*Tel: 0228/732494 (Work) 0228/238452 (Private) *
***********************************************************************
No programmer works nine to five, exept those on the nightshift.
SCOTT I CHASE
>
>>Before getting to the details, I have one general piece of advice:
>>build a prototype as quickly as possible after you have settled on
>>basic design parameters. Don't try to make it fancy. Just throw
>>it together and test it. You will figure out quickly what the
>>problems are, if any, and how best to spend your effort on the
>>final product, if the prototype itself isn't good enough to do the
>>job.
>
>A wire table and a few quick calculations will tell this person whether or
>not a Helmholtz coil will do the job here. Unless he just wants to acquire
>coil-winding expertise, there's no point in building it if it won't work.
Agreed. I didn't mean that he should build the coils before calculating.
I'm with Norm: "Measure twice, cut once". What I meant was that once he
is convinced that Helmholtz coils will work, (that he doesn't need an
full-blown electromagnet to get the field-strength he wants), that the
details of the design need not be worked out in gory detail before
building a prototype. Often, there are practical design considerations
that are not apparent until after you have tried to build one. I was
just encouraging him to work out the bugs as quickly as possible, and
not to get hung up on perfection. By building a quick-and-dirty prototype,
say winding one by hand rather than machine, for example, he may find
that it isn't necessary to get too sophisticated to build a device which
meet his needs.
Tommy Nordgren
|> Remember also that the field will be temperature dependent. Hot coils
|> have more resistance than cold coils. So you need to control for
|> temperature or continuoiusly calibrate the coils during or between
|> experimental runs.
This subproblem is easiest handled by powering the coil with a
constant current generator.
-------------------------------------------------------------------------
Tommy Nordgren "We hold these truths to be self-evident"
Royal Institute of Technology "In this sign conquer."
Stockholm "The eagle has landed."
f85...@nada.kth.se "Please mister, could I have a cracker
to my onthatherium."
--------------------------------------------------------------------------
Superconductivity Publications
: I'm looking for people who could give me information on the design
: and construction of a Helmholtz coil pair, or who could point me to
: appropriate references (books/journals, or even knowledgeable people).
General Electric has commercialized an MRI magnet using a Helmholtz
design. A prototype is in operation at Brigham and Women's Hospital
in Boston. The biggest advantage of the system is that it allows a
surgeon to operate on a patient while the MRI unit is on line.
Combined with focused ultasound the system will dramatically alter
surgical procedures.
We published a 12-page article on the subject in the January 26, 1994
issue of Superconductivity News. The following excerpts are from
pages 4 & 5 of that issue.
The Key to MR Fluorscopy:
A Pair of Idential Magnets
The critical factor enabling the surgeon to operate with the advantage
of real-time MRI is the space provided between a set of identical,
highly tuned magnets, a design called a Helmholtz pair. This design
consists of a pair of flat, circular coils, having an equal number of
turns and equal diameters, arranged with a common axis and connected
in series. Helmholtz pairs provide a more nearly uniform magnetic
field than a single coil. Bob Cordini, GE Medical System's manager of
marketing for image guided therapy programs, describes the
configuration as two donuts connected by a structural separation. He
added, "The design is quaite a bit more difficult than conventional
MRI magnets, you are winding two separate sets of coils that have to
be electrically connected."
Holding the Magnets Apart
The structural suppport separating the magnets is no trival matter
since the magnetic forces pulling them together are very strong.
"There is a lot of twisting force which must be designed around to
keep the magnets parallel," Dake explained.
[Dake is plant manager for GE's Florence, SC MRI magnet facility]
Maintaining a Stable, Gradient Magnetic Field.
MRI became possible only through the ability to control gradients in
the magnetic field. Within a single solenoid this is not difficult.
One can envision how it would be easy to maintain a stable z-axis
field gradient in a Helmholtz pair but, as Morrey Blumenfeld, general
manager of image-guided therapy programs at GE Medical Systems
comments, "It is difficult to attain x and y axis gradients and keep
the field linear." This difficulty was overcome through the
integration of new proprietary magnet technologies and software
capabilities.
"The design of the magnets is base don new concepts in magnetic field
gradient control," Dake said. "You have to be able to project the
field into an open space." The magnetic field in terms of gauss/cm
that can be attained depends pn the projection distance, the magnetic
field strength, and the area/volume covered by the field.
END of EXCERPTS
My advise -- review the patent literature for GE's MRI magnets.
C. James Russell
--
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Ian D. Gay
>Jeffry T Urban (ju...@andrew.cmu.edu) wrote:
>: I'm looking for people who could give me information on the design
>: and construction of a Helmholtz coil pair, or who could point me to
>: appropriate references (books/journals, or even knowledgeable people).
[wondrous P-R blurb deleted]
That's nice, but couldn't you also have told us the field achieved,
and whether the coils are superconducting?