Consider a series LCR circuit. Once power source is removed, the electrical energy oscillates for some time before damping out completely. I want a LCR circuit such that 1) it has high resonance frequency , say 1 GHz and 2) it oscillates for some time say 1 min.
Consider following numbers. To achieve 1 GHz, L and C must be very low. Let C=1 pF and L=25nH. This gives us resonance frequency around 1 GHz. At such high frequency the inductor wire will pose some resistance, let us assume R=0.001 Ohm, even though it is likely to be more. The attenuation factor $\alpha=R/2L$ is going to be high, which means the oscillations even if under-damped, will not sustain even for a second. Clearly there is a trade-off between high frequency and longer oscillation.
Is there a way to achieve both? It is ok even it is achieved without removing the power source, however, note that the voltage source is 10-100KV DC. Just keeping the LCR connected to the power source will not result in oscillations, in my understabnding.