AC source resistance problem while simulating transformer in LTSpice
Since you want to build it, I would discard this circuit. Spehro's answer shows you why.

I would just like to show you a circuit that could achieve what you need in a more practical way.



You can see your sensor, the circuit is just an opamp inverting amplifier. You control the gain with the ratio R5/R2, 10 in this case. If you were to build the circuit, it would probably be a good idea to add 100nF in parallel with R4, and of course also in parallel with the supply of the opamp.

R3 and R4 form a voltage divider to add an offset of half the supply so that you dont clip the signal on the negative semiperiod, C1 is just ac coupling the input signal.

You can see a sample waveform below:



The blue trace is the input signal, the red one is the output signal. The output of the opamp is also very low impedance, so you could drive other stages/detectors with it.

One point to note is that C1 should be adjusted for the minimum frequency you are interested in. Right now, with this value, your bandwidth starts at around 2Hz as you can see in the following AC plot:



If you don't need such a low frequency, you can decrease the value of C1 proportionally.