Multipliers crossed-field

Two additional special purpose multiplier designs are also quite common. The first is the crossed-field device [5.138] where a magnetic field is used in conjunction with a specified electrostatic field to force high-energy electrons into... 

The problem now reduces to finding how ra is related to the experimental parameters. The gas supply functions for different tip geometry have already been discussed in Section 2.1.2 and they are given by eqs (2.9), (2.11) and (2.12). zs is the total gas supply function Z multiplied by sa/A where sA is the cross-section of a surface atom in capturing an incoming gas atom, and A is the total area of the gas supply function. For a large field enhancement factor, = aF2/2kT, zs can be approximated by... 

During slow collisions, the main contribution to the charge transfer cross-section is made by the impact parameters which exceed the size of a neutral atom. In this case, the potential barrier for tunneling is mainly formed by the electric field of the multiply charged ion in the vicinity of the neutral atom (Fig. 8). This field is equal to F = zjR2. The probability of... 

The expansions in even powers of normal frequencies are of special interest, because they provide means for obtaining explicit relations between the equations of motion and the thermodynamic quantities, through the use of the method of moments The sum of over all the normal vibrations can be expressed as the trace, or the sum of all the diagonal elements, of a matrix H" obtained by multiplying the Hamiltonian matrix H of the system by itself (n — 1) times. Such expansions thus enable us to estimate the thermodynamic functions and their isotope effects from known force fields and structures without solving the secular equations, or alternatively, to estimate the force fields from experimental data on the thermodynamic quantities and their isotope effects. The expansions explicitly correlate the motions of particles with the thermodynamic quantities. They can also be used to evaluate analytically a characteristic temperature associated with the system, such as the cross-over temperature of an isotope exchange equilibrium. Such possible applications, however, are useful only if the expansion yields a sufficiently close approximation. The precision of results obtainable with orthogonal polynomial expansions will be explored later. 

The avoided crossing of the sideband state is the purely static field avoided crossing multiplied by the amplitude of the m-th sideband state. The size of the... 

Some of the types of contributing elements combined in Eq. (1) can give rise to potential pieces that are not additive. These would involve products of property or parameter values for more than two molecules, and these are often referred to as cooperative or nonpairwise additive elements. A simple illustration is in the electrical interaction contributions. While the interaction of permanent moments is pairwise additive, involving products of moments of only two different molecules at a time, the polarization energy can have a cooperative part. For some cluster of the molecules A, B, and C, the dipole polarization energy of A will be the polarizability of A, Ka, multiplied by the square of the field experienced at A, F. That field is a sum of contributions from B and C ( F = Fb + Fc) proportional to their multipoles, and its square has a cross term, FbFc, involving a multipole of B times a multipole of C. The net interaction element includes Ka FbFc. thereby giving an overall A B C or three-body term. Mutual or back polarization can be shown to produce contributions up to A-body for a system of N species. 

Even if we computed the microscopic velocity field in the x, y and z directions, we only considered the macroscopic averages in the y and z directions, as no heterogeneity is considered in the x-direction. The macroscopic fluxes were calculated by averaging the microscopic velocities over 50 time steps, over five sites in the z-direction, and over half-cross sections of the micropore matrix and of the crack, multiplied by the respective mean water contents. 

Two of the three laser ionization methods have already been discussed, namely one-photon PI and multiphoton MPI. The third type is resonance enhanced MPI, or REMPI. In the latter method the laser is tuned so that an intermediate state of the molecule is excited with one, two, or perhaps three photons. The excitation of the intermediate state determines the overall cross section for the process because the absorption of additional photons to reach the ionization continuum is generally rapid. In contrast to PI and MPI, REMPI is state selective if the absorption process is resonant between two bound and reasonably long-lived states of the molecule. It is an extremely sensitive method for product detection because the result of the REMPI process is an ion which can be detected with near 100% efficiency. Not only is the ion collection efficiency of the detector (e.g., by channeltron electron multiplier or a multichannel plate detector) extremely high (ca. 50%), but all ions regardless of their initial velocity vector can be collected by the application of appropriate electric fields. This is a major advantage... 

In addition, several examples of application were cifed. These include phenomena such as, ac field-induced sfabilizafion of resonances, or long-time NED and ifs relafion fo issues of irreversibilify at the quantum level, or the profile of phofoabsorpfion cross-secfions for resonance fo resonance fran-sifions, or fhe fime-dependenf coherenf excifation and multichannel decay of multiply and inner-hole excifed sfafes, or aspects of the physics of fhe... 

A common experimental arrangement for the study of molecular Rydberg states is depicted in Fig. 5.31. The output beams of two pulsed narrow-band dye lasers, pumped by the same excimer laser, are superimposed and cross the molecular beam perpendicularly. The fluorescence emitted from the intermediate level (u, J ) or from the Rydberg levels (u, 7 ) can be monitored by a photomultiplier. The ions produced by autoionization (or for levels slightly below IP by field ionization) are extracted by an electric field and are accelerated onto an ion multiplier or channel plate. This allows the detection of single ions. In order to avoid electric Stark shifts of the Rydberg levels during their excitation, the extraction field is switched on only after the end of the laser pulse. Experimental details and more infor-... 

---