Synchronous molecules

Central to the understanding of the operation principle of a Stark decelerator are the concepts of a synchronous molecule and of phase stability. Returning to Figure 14.6, we call the position z of a molecule at the time when the fields are switched the... 

As a result, the average force, F, acting on the synchronous molecule is given by... 

FIGURE 14.7 Phase-stability diagram for OH(7 = 3/2,Mfi = —9/4) radicals when the decelerator is operated at a synchronous phase angle ())o = 0 ° (upper panel) or 4)o = 70 ° (lower panel), with Vi the velocity of the nonsynchronous molecule along the longitudinal coordinate z and 4) its phase. The value = 0 corresponds to the velocity of the synchronous molecule. The positions of the electrodes of the decelerator are indicated by dashed lines. (From van de Meerakker, S.Y.T. et., Annu. Rev. Phys. Chem., 57,159-190, 2006. Copyright (2006) by Annual Reviews www.annualreviews.org. With permission.)... 

FIGURE 14.8 Longitudinal acceptance of a Stark decelerator for OH radicals for different values of the synchronous phase angle Here is the velocity of the nonsynchronous molecule along the longitudinal coordinate z and is its phase. The value = 0 corresponds to the velocity of the synchronous molecule. 

Because we now have the potential seen by the molecules as a function of both position and time, we can solve the equation of motion numerically for any molecule, synchronous or not. Let us define N to be the minimum number of stages required to stop the synchronous molecule of mass M and initial speed Mq, through the relation Wo = MUq/(2N). Figure 15.15 shows the result of such a calculation for the case where L = 2/3D, d = 1/15D, and N = 80, and the turn-on and turn-off points are A and B in Figure 15.14b. The thick red line shows the speed of the synchronous molecule versus time, while the thin blue line shows how the speed changes with time for a molecule that has the same initial speed as the synchronous molecule but starts out ahead by D/15. The deceleration of the synchronous molecule appears to... 

For small-amplitude oscillations about the synchronous molecule, the motion is harmonic. Expanding the right-hand side of Equation 15.29 in a Taylor series about z = 0, gives d z/dt - (W (zon) - Wizos))z/(MD) = 0 where W ia) = dW/dz evaluated at z = a. The angular oscillation frequency for small-amplitude axial oscillations is therefore... 

By definition, the synchronous molecule travels a distance L in the time interval between two successive switch times. The change in kinetic energy per stage AK (po) = —AW (j>o) for a synchronous molecule with phase o and velocity vq at a certain switch time is then given by the difference in potential energy at the positions o and o + it ... 

Fig. 9.10. Observed and simulated TOF profiles of a molecular beam of OH radicals exiting the Stark decelerator when the deceierator is operated at a phase angie of 70° for a synchronous molecule with an initial velocity of 470m/s (o), 450m/s (6), 430 m/s (c) and 417 m/s (d). The molecules that are accepted by the decelerator are split off from the molecular beam and arrive at later times, and with the final velocities as indicated, in the detection region. (Reproduced from S.Y.T. van de Meerakker et with permission. 2006 by Annual Reviews www.annuaireviews.org.)...

Fig. 9.11. Scheme of the end of the decelerator, the buncher and the detection region. The calculated longitudinal phase-space distribution of the ammonia molecules is given at the exit of the Stark decelerator, at the entrance and exit of the buncher and in the detection region. The position and velocity are plotted with respect to the synchronous molecule. The solid curves show lines of equal energy in the buncher potential (compare to Fig. 9.7). (Reproduced from F.M.H. Crompvoets et al. with permission. Copyright the American Physical Society.)...

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