Steel jacket on electromagnet at 1 KHz is bad news. You will probably have to design an electromagnet.

Make decision on core. Possible candidates are 2 mil silicon steel, metglas, nickel iron or ferrite.
I would start with ferrite. My belief is that it's easier to work with, more readily availiable and will probably work.

Design electromagnet. Mechanical forces on ferrite may be significant.

Either calculate inductance or build electromagnet and measure.

Select capacitor to resonate with electromagnet inductance.
Remember capacitor has to be rated for AC application

Calculate wattage that electromagnet can dissipate.

Build or obtain 1 KHz oscillator or amplifier and function generator.

You need the lowest inductance possible to minimize power.  Ferrite is a good chaice.  Since it is a ceramic it has high resistance and low eddy current effects.
You need to get the system to resonate at 1kHz. Remember R-L-C.
How large of an area do you need?  This will need to be a very strudy structure.  You will want the coils to be internally cooled and fully potted in resin.  It will be trying to self destruct.

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Rust never sleeps
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Thanks both CarlPugh and EdStainless!

Because I am going to use the magnet under an optical microscope, so mechanical vibration is not acceptable during operation, I will probably use a core material with low magnetostriction. (e.g. http://www.jfe-steel.co.jp/en/products/electrical/jnex/list.html)

For the coil, it seems there are two approaches:
(1) large number of turns so that I will get enough field, but of course the impedence will get very high at high frequency, so a high voltage (+/-500V) power supply with moderate current, say 3A, is a must.
(2) small number of turns but using a power supply with high current output, say >10A. this will solve the problem of high inductance of coil but a high current supply is needed.

As I am a newbie in electricity, which way, high voltage or high current power supply, is better and easier to get?

By the way, as the magnet is not only working at 1kHz, but from the range of 500Hz to 5kHz, what should I pay attention to in the RLC resonance? (actually I am lack of knowledge about resonance and impedance matching with the power supply, any suggested reading or website?)

Thanks a looooooooooooooooooooooooot!

Does the frequency have to be continously adjuatable or can it be in steps?.
Steps where the magnet is turned off and the capacitance is changes for a different frequency is much easier. (If frequency does not have to be exact)

High current operation requires that skin effect be taken into consideration, but hollow tubing using water cooling can be used.
Low current operation has problems with cooling.
Which is best? Who knows, do a design using high current and low current and select the lowest cost approach.

It will probably be simplier to purchase an amplifier & function generator or high power oscillator and not attempt to use a DC power supply.

Most basic AC electronic text books have chapters on resonance.

It may be worthwhile going to Ceramic Magnetics web site, they make custom ferrite cores.

Mechanical viberation is an interesting problem. Any magnetic material near the magnet gap will have a force on it. Also any conductive material near the magnet gap may have a force on it?

It's my opinion (not backed up by any solid evidence) that ferrites have low magnetostriction.

Now that I think about it I am not sure that you need any core at all.  Why not 'air core'?  Think of a long solenoid with a window in it.
You high freq you want as much of the structure non-conductive as possible.  Use glass/epoxy for structures.  How much motion will this cause in you support table and lens assembly?  You may need to put the final unit into a steel tube to shield the external field.

= = = = = = = = = = = = = = = = = = = =
Rust never sleeps
Neither should your protection
http://www.trent-tube.com/contact/Tech_Assist.cfm