Reduced cyclotron frequency

Rearranging Eqnation 5.6 gives a quadratic equation in o) that can be solved to give the reduced cyclotron frequency... 

This quadratic equation has two solutions, the first of them representing the reduced cyclotron frequency co+... 

Microwave discharges at pressures below 1 Pa witli low collision frequencies can be generated in tlie presence of a magnetic field B where tlie electrons rotate witli tlie electron cyclotron frequency. In a magnetic field of 875 G tlie rotational motion of tlie electrons is in resonance witli tlie microwaves of 2.45 GHz. In such low-pressure electron cyclotron resonance plasma sources collisions between tlie atoms, molecules and ions are reduced and the fonnation of unwanted particles in tlie plasma volume ( dusty plasma ) is largely avoided. 

Studies to improve the experimental precision for ae focus on the understanding and control of this cavity influence on the cyclotron frequency. One approach is to reduce the Q of the cavity [9]. In another attempt Mittleman et al. produced and studied a many-electron (kiloelectron) cluster in the trap, which magnifies the shift of the cyclotron frequency [10]. Gabrielse et al. are studying the use of a cylindrical cavity where the cyclotron frequency shift can be calculated analytically and is hence under better control [11]. The eventual reduction of experimental uncertainty by about an order of magnitude is the goal of these experiments. 

A second improvement was that we measured the cyclotron frequency in the precision trap simultaneously with the Larmor frequency. This reduces to a large extent possible errors induced by a temporal variation of the magnetic field which occurs in superconducting solenoids typically at a level of 10-8 per hour. In the final experiment we measure the rate of spin Hips at different ratios of the Larmor- and cyclotron field frequencies. An example is shown in Fig. 10. The linewidth is of the order of 10-8 and the g factor can be determined with a statistical uncertainty below 1 ppb [19]. 

One can find the velocity veb, which corresponds to i + veb x. 6 = 0. It reduces the particle motion to = 0 x B, which is rotation around the magnetic field lines (Fig. 3-6). The frequency of this rotation is the so-called cyclotron frequency ... 

A different approach to probe the ion-neutral potential involves the analysis of collision-broadened ion cyclotron resonance line shapes. For ions undergoing elastic collisions, the power absorption curve is Lorentzian in shape with a half-width at half-maximum equal to the collision frequency (J, which is then simply related to the reduced collision frequency, the diffusion cross section, and the ion mobility. For a series of nonreactive alkyl cations in methane, excellent agreement is found between experimental values for these quantities and theoretical values predicted from the Langevin model.H Unexpectedly, this finding may be interpreted to suggest that other mechanisms for collision broadening, namely inelastic collisions and, specifically, collisions involving complex formation, appear to be unimportant. ... 

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