Helical Resonator Design

I am designing a helical resonator (quarter wave), for plasma discharge. I designed it for 150 MHz, with outer shield of 77 mm (3 inches) diameter according to formulas given in papers. The resonator has inner coil with 4.8 turns with pitch 2.16 turns/inch.

I am getting resonance frequency at 133 MHz and also at 369 MHz (third harmonic). This is OK as my number of turns are little higher.

Theoretically I should get 50 ohms match at 1/3 of turn. But when connect at theoretically calculated position it is showing VSWR of 15. I am getting VSWR= 2, at a location very close to ground and it is not possible to go lower.

It seems that Q of the resonator is much higher than theoretical value. This is impossible, something is wrong. Tried changing coil parameters but could not impedance matching. Please suggest what to do next.

Matching which real load?

Q factor equation of the helical resonator in most of the cases is referring to unloaded-Q, which can reach very high values.
For best impedance matching, instead using just a wire connection to tap the resonator, you have to use a series trim capacitor, and adjust its capacitance in concordance of various turn ratios (perhaps 1/3 ratio should be fine), until you get the best VSWR.
If the helical resonator is part of a multi-pole helical filter, this capacitance will be slightly different getting best VSWR, or getting the requested filter characteristics.