Vibrating Wire Test 23 March 2007 A wire of mass per unit length μ under tension T, of length L held fixed at each end has a fundamental vibration frequency f 1 = 1/(2L) √(T/μ) A magnetic field, in combination with an alternating current through the wire will create an oscillating transverse force on the wire. If the AC frequency matches one of the harmonic frequencies of th wire, a resonant condition occurs.

Vibrating Wire Test By sweeping frequency of AC through the wire, the amplitude of vibration and its phase relative to the driving force trace out resonance response. With thin, flexible wire the damping is mainly from friction of air and the Q is quite high, making method sensitive to weak fields. Size and sign of resonance depends upon location of applied periodic force. Conversely, measuring size/sign of many harmonics allows the B field distribution along the wire to be calculated.

Vibrating Wire Test Scrounged from Wayne Faszer 100um Cu-Be wire plastic V-pulley c/w mount 96 g weight Collected and assembled by Peter H21A1 optical limit switch (detects wire motion), 9V battery and resistors var. frequency sine-wave generator amplifier scope DVM

Vibrating Wire Test: apparatus Wire position sensor (H21A1 optical limit switch) mounted on x-y stage. Cu-Be wire

Pulley Wire Fixed end C-magnet 96g weight DVM Scope

Scope readout: 25 Hz driving force

Vibrating wire test First test using earth’s mag. field (0.52 Gauss vert.) Length of wire 2.28 m, tension 96 g-wt  calc. fundamental frequency 27 Hz Substantial signal seen: Vrms ~ 20 mV for 0.1A current through wire See 25.4 Hz, FWHM < 1 Hz Second test using C-magnet -- placed 3/5 of distance from sensor end to far end -- at wire: approx. 2-3 Gauss max. with ~50cm FWHM

Vibrating Wire Test Approx. to Fourier components good enough to reveal magnet location, approx. length of field Could easily could have sensed 10x smaller field say 3 G x 50 cm / 10 = 15 G-cm (also ~sens’y quoted in Temnikh article) If this can be achieved in a quad of r=75mm and pole-tip field 2.4 kG and eff. length 30cm,  find magnet centre to within 15/(32x30) = 16 um (relative to ??) Next: test in a section of DRAGON separator?