Generating var. freq. magnetic fields 0.2 - 2 MHz or higher

[OldN00b]

I need to generate rather strong EM AC fields over quite a frequency range. What I have in mind is a coil at most the size of an induction heater, and a comparable field strength. There are various oscillator designs for such a L-C oscillating setup, but none of them are variable-frequency. The difficulty lies in due to the impracticality of having such a large C variable over such a long range.

My coil would ideally just be a single winding with a diameter of 1 to 3 cm (about 1 inch max.). This to be able to maximise the current and hence the field strength.

The goal is to have a high as possible field strength (2 Tesla or higher would be ideal) and to have an as wide as possible frequency range, starting at 200 kHz and at least to 2 MHz but up to 20 MHz would be good too.

I'm looking forward to your suggestions. Please suggest any outlandish idea, as long as it works, because money is no object, this device may cost 50 grand (USD) in parts.
I already know how to generate much higher fields than 2 T at a fixed frequency, using a capacitor bank and a triggered spark gap.

To recap: Insanely high AC magnetic field strength, very wide, VARIABLE frequency range, money is no object (well, 100,000 USD max. for the time being).

I am fully aware of the craziness of building such a device, I know full well that the coil for ex. would need water cooling and that a high voltage power source will be required. And that shielding will be required to stay within the RF emission laws. Quite a few engineering challenges along the way but that's all fully anticipated. I'm willing to construct my own variable capacitor. Thank you for your suggestions. Just to show that I'm already seriously tinkering with stuff for this project, attached a 150 uF/2KV high-quality, high-current cap I made by hand-soldering nearly 1000 Cornell Dubilier C's in parallel. This for my fixed-frequency device. Just that cap cost me 5 grand. Just as a small test project.

The "winning idea" will be implemented ASAP and progress reports will be in this thread.

[Rerouter]

As money is not a big objection, lets begin with the 200K - 2M, a 10:1 tuning range, for this, you may be able to use a saturatable reactor approach, partially saturating the core to reduce the apprent inductance, to expand your range

Now a 3cm coil will need crazy amps, so instead you could do a flux concentrator. and use a larger coil on both ends, meaning your currents are lower, and your coils can be bigger.
e.g. https://www.quora.com/Can-you-use-a-shaped-magnetic-material-to-focus-and-concentrate-earths-magnetic-field

instead of starting out with 1m like in the example, perhaps a 15cm coil of 50 turns, with a C shaped magnetic core and your sample is loaded in to the gap, this should allow stupidly high tesla in your small area for not much current. meaning most of the easier wide band approaches are easier to realize, and your back down towards mains outlet power levels.

[OldN00b]

There were many replies in this thread with a lot of helpful suggestions, why has everything been removed??

[MK14]

There were many replies in this thread with a lot of helpful suggestions, why has everything been removed??

https://www.eevblog.com/forum/projects/how-to-generate-strong-variable-freq-ac-magnetic-field/

[T3sl4co1l]

To come up with proposals, we'll need a clearer definition of waveform and "variable".

Tim