Very low power to feed up primary coil for Wireless Power Transfer

Hi
i am working on wireless power transmission . So far i have made couple of coils with wire gauge (20, 22, 30) and with different sizes and shapes.
I am feeding the primary coil with my function generator (1MHz, 10V peak-to-peak) and towards the receiving end i am barely getting enough power to barely light up an LED. I have experimented different coil shapes and even increased the frequency to 10MHz but of no use.
I know that i need MOSFETs to boost up the power to primary coils, but i am a little confused on how to proceed and which MOSFETs to choose from.
Plus, someone also mentioned that i should use a DC power supply with lets say around (50V) and use oscillatory circuit to feed it to MOSFET (Driver - then MOSFET IC).
i was told that in that way i can get a great power to excite the coil.
Actually i am more into RF and RF circuit design, i designed the coils and matched the frequency using my previous antenna design skills, but the Analog circuitary to feed it up is a nightmare for me.
Any help in this regard shall be appreciated and will get me going further

cheers

P.S.
i am also attaching a basic picture of my Experimental set-up (that will give you a better picture)

The first thing to do is to resonate (tune) the coil to your working frequency on both the transmission and reception coil. At the moment the coils are offering a significant inductive impedance, reducing the transmission power and reception voltage. Also try matching the transmission coil to the output impedance of the generator. One way to try is to get a 100 pF and a 1000 pF capacitors, feed the signal across the 1000 pF and connect the live end of the coil via the 100 pF to the live point and return the other end to the earthy end of the 100 pF. This way you have put a 10 :1 tap on a tuned circuit to stop it being damped too much. Swing the frequency and see if you can detect a peak in the received signal. This will be your operating frequency. Repeat with the capacitors on the receiving coil, but you will now have to adjust the shape/number of turns of the coil to get it to tune to the same frequency.
Once both the coils are peaked the energy transfer will still be puny, but it will have taken some of the uncertainty out of the experiment.
Frank

thanks a ton for your reply. i am in my lab and will start working on it right away.
i will keep my status updated.

cheers

---------- Post added at 07:54 ---------- Previous post was at 07:18 ----------

Dear Chuckey
still lost, i did the series/parallel capacitor combination both towards the transmission and receiving end, but for some reason it gives absolutely the same result. The LED lights up exactly with the same intensity . a rough schematic might help, im really lost here

cheers