Velocity-acceleration correlation experiment

In velocity-change NMR the variables q and q 2 replace the axes ki and kz in Fig. 5.4.5, and ui and V2 replace r and r2 (Fig. 5.4.12). In a coordinate frame rotated by 45° the difference coordinate corresponds to acceleration a and the other to velocity v, so that this exchange experiment can be read as a velocity-acceleration correlation experiment. Following the coordinate transformations (5.4.21) for position-change spectroscopy, the following coordinate transformations apply for velocity-change spectroscopy. 

As ambient air pressure is increased, the mean droplet size increases 455 " 458] up to a maximum and then turns to decline with further increase in ambient air pressure. ] The initial rise in the mean droplet size with ambient pressure is attributed to the reduction of sheet breakup length and spray cone angle. The former leads to droplet formation from a thicker liquid sheet, and the latter results in an increase in the opportunity for droplet coalescence and a decrease in the relative velocity between droplets and ambient air due to rapid acceleration. At low pressures, these effects prevail. Since the mean droplet size is proportional to the square root of liquid sheet thickness and inversely proportional to the relative velocity, the initial rise in the mean droplet size can be readily explained. With increasing ambient pressure, its effect on spray cone angle diminishes, allowing disintegration forces become dominant. Consequently, the mean droplet size turns to decline. Since ambient air pressure is directly related to air density, most correlations include air density as a variable to facilitate applications. Some experiments 452] revealed that ambient air temperature has essentially no effect on the mean droplet size. 

The only gross mode that is normally observed is the rotational n = 2 instability. The observed stable period before the mode onset is consistent with the FRC increasing in angular velocity until it crosses a threshold for instability predicted by a Vlasov fluid code. The angular acceleration could be due to an external torque perhaps applied by plasma outside the separatrix through viscosity.Another cause of acceleration could be net angular momentum carried by particles diffusing across the separatrix. This particle loss model predicts that the onset of the instability should occur when about half the particles are lost. This prediction is consistent with the experiment. Since the external torque or other sources of rotation are also possible, better correlation between experiment and theory is needed to properly understand this issue. However, if the FRC stable period Xg (time before mode onset) continues to scale with the time required to lose half the particles, then particle transport, not the rotational mode, will limit the reactor potential of the FRC. 

The plate dent test is described in Chapter 5 and in reference 35. The plate dent test consists of detonating a cylindrical charge of explosive in contact with a heavy steel plate and measuring the depth of the dent produced in the plate. The depth of the dent correlates with the C-J pressure as shown in Figure 2.21 for most explosives. The depth of the dent in the plate dent experiment is much greater for tungsten or lead-loaded explosives than expected for their observed detonation pressure. For example, a 60/30/10 volume percent RDX/Pb/Exon at 4.6 g/cc has a detonation pressure of 150 kbar as determined by metal plate acceleration data and 345 kbar as determined by the plate dent vs. C-J pressure correlation described in reference 35. The experimentally measured detonation velocity is 0.5012 cm//iis. The BKW-calculated C-J pressure is 270 kbar and velocity is 0.5096 cm/)us. Similar calculated results are obtained whether the lead is considered as compressible or incompressible and whether the lead is in temperature and pressure equilibrium with the detonation products or is in pressure equilibrium alone. 

---