Threshold field

As shown in Fig. 4.9, these studies provide evidence that the breakdown was characterized by a fixed threshold stress of 11 GPa and a fixed threshold field of 2.8 X 10 Vm Once the threshold stress is exceeded, the conduction is controlled by the field and is independent of the stress. The threshold field is in reasonable agreement with the field of 7 x 10 V m below which a recovery from breakdown is observed when the field decreases due to the... 

At higher threshold fields, the banana leaf and most other B7 textures observed for MHOBOW also convert irreversibly to bistable blue, though the picture is still complex, with unusual textures still seen in the cell. Our interpretation of this behavior, however, is simple. The bistable blue texture observed for MHOBOW is obtained from an SmCsPF conglomerate the target of the molecular design and synthesis effort. 

Field ionization can also be enhanced by photons. Tsong et al.43 searched for this effect and found that Ar field ion current near the threshold field of field ionization from an aluminum oxide tip could be enhanced by a factor of about 5 when the tip was irradiated with 4.16 eV photons from laser pulses of 2 p,s width at a pulse repetition rate of 25 Hz, or a duty cycle of only 0.005%. As the photon energy is much too small to... 

These results, Eqs. (6.35) and (6.36), are only valid for m = 0 states. In higher m states there is a l/(x2 + y2) centrifugal potential keeping the electron away from the z axis, and the centrifugal barrier raises the threshold field of m 0 states.16 Specifically, for m 0 states the fractional increase in the field required for ionization, compared to an m = 0 state of the same energy is16... 

Using this energy we find a threshold field... 

For the blue states it is not possible to estimate simply the threshold field. However, blue and red states of the same n and m=0 often have threshold fields differing by a factor of 2. 

When field ionization threshold curves such as the one shown in Fig. 7.4 are measured for many states, they can be plotted together to exhibit the n dependence of the ionization threshold field. In Fig. 7.5 we show a plot of the threshold fields (50% ionization) for the Na m = 0, 1, and 2 states obtained with a 0.5 / risetime field pulse similar to the one shown in Fig. 7.1(b).8 In Fig. 7.5 it is apparent that, while the threshold fields of the m = 0 states are described by Eq. 

Having considered the connection between the multiphoton resonances and the microwave threshold field for the K (n + 2)s —> (n,k) transitions, it is now interesting to return to the analogous n — n + 1 transitions which are responsible for microwave ionization and consider them from this point of view. We start with a two level description based on the extreme n and n + 1 m = 0 Stark states, a description which is the multiphoton resonance counterpart to the single cycle Landau-Zener model presented earlier. The problem is identical to the problem... 

Pillet et al. observed that adding small static fields dramatically reduces the microwave fields required for the ionization of Li.19 For example the application of a static field of 1 V/cm lowers the 15 GHz ionization threshold of the Li 42d state from 200 V/cm, to a broad threshold centered at 20 V/cm, a field only slightly in excess of E = 1/3n5 = 13 V/cm. The threshold field 200 V/cm corresponds to the hydrogenic threshold field of 1/9 n4, which will be described shortly. A small field has virtually no effect in a single cycle Landau-Zener model, but its dramatic... 

The first measurements of microwave ionization in any atom were carried out with a fast beam of H by Bayfield and Koch1, who investigated the ionization of a band of approximately five n states centered at n = 65. Using microwave and rf fields with frequencies of 9.9 GHz, 1.5 GHz, and 30 MHz, to ionize the atoms they found that the same field was required at 30 MHz and 1.5 GHz to ionize the atoms, but that a smaller field was required at 9.9 GHz. The measurements showed that at n = 65 frequencies up to 1.5 GHz are identical to a static field. Later, more systematic measurements have confirmed the initial measurements and have allowed significant refinements of our understanding. In Fig. 10.16 we show the ionization threshold fields (in this case the field at which there is 10% ionization) of H in a 9.9 GHz field.21 The ionization fields are plotted as n4E vs n3a>, and they bring out two factors. First, at low frequencies the field required is l/9n4, the static field required to ionize the red n Stark state of m n. Second, as shown by the scaling of the horizontal axis, the required field drops below l/9n4 as the microwave frequency approaches the interval between adjacent n states, 1 In3. 

As o) increases further above 1 In3 a single photon drives the initially populated state closer and closer to the ionization limit, and ionization occurs with the absorption of fewer photons. Few photon processes are well described by lowest order perturbation theory, which shows that the rates are proportional to E2N, where N is the number of photons absorbed. For small N such processes are not well described by a threshold field, and it is not meaningful to discuss ionization threshold fields in this case. 

While ionization by linearly polarized fields has been well studied, there is only one report of ionization by a circularly polarized field, the ionization of Na by an 8.5 GHz field.36 In the experiment Na atoms in an atomic beam pass through a Fabry-Perot microwave cavity, where they are excited to a Rydberg state using two pulsed tunable dye lasers tuned to the 3s — 3p and 3p —> Rydberg transitions at 5890 A and —4140 A respectively. The atoms are excited to the Rydberg states in the presence of the circularly polarized microwave field which is turned off 1 fis after the laser pulses. Immediately afterwards a pulsed field is applied to the atoms to drive any ions produced by microwave ionization to a microchannel plate detector. To measure the ionization threshold field the ion current is measured as the microwave power is varied. 

A much higher circularly polarized field is required to ionize the atoms than a linearly polarized field, as shown by Fig. 10.21, a plot of the threshold fields, where 50% ionization occurs, for linearly and circularly polarized 8.5 GHz fields. As shown by Fig. 10.21, the circularly polarized microwave ionization threshold field is very nearly E = l/16n4, the same as the the static field required to ionize a Rydberg Na atom and much higher than the field required for ionization by... 

Fig. 10.21 Ionization threshold fields for linear (+) and circular ( ) polarization as a function of n when Na atoms are excited in the 8.5 GHz microwave field (from ref. 36).

All sorts of biological particles of different effective complex dielectric constants behave similarly in an electrolyte medium. Figure 5 illustrates this fact. Neumann and Rosenheck s (AO) results on chromaffin vesicles are combined with E. coli data obtained by Sher and erythrocyte data obtained by Sher and silicon particles (full circles), also by Sher (A5). The total material fits convincingly the solid line of slope -1.5 which is demanded by the theoretical requirement that particle volume must be inversely related to the square of the threshold field strength mentioned above and discussed in greater detail elsewhere (Schwan and Sher (5A)). 

The dashed curves in Figure 5 pertain to another model. It is assumed that the threshold of a cellular response or destruction is reached when the induced membrane potential reaches the dielectric breakthrough level. This level may well be in the range of 0.1 to 1 V across the membrane, corresponding to membrane field strength levels from 100 KV/cm to one million V/cm. The inverse relationship of the threshold field level in the medium with the particle diameter follows from the equation... 

Figure 5. Threshold field strength values as a function of particle size (49).

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