Critical energy fluence

In its usual form the critical energy concept is really a critical energy fluence concept and is expressed as... 

In addition to exptl contradictions the critical energy concept is also subject to fundamental theoretical difficulties. For example, as pointed out by Stresau Kennedy (Ref 54a) Macroscopic models, such as Walker Wasley s concept of critical energy fluence and Pastine, Bemecker Bauer s concept of critical thermal energy, do not explicitly address the point that the concentration of the energy in hot spots is essential to initiation, and its consequence, that the temp of the hot spot plays a significant role in the initiation process. It seems that the distribution, rather than the density, of the thermal energy should be expected to be decisive in the initiation process ... 

The quantity p U [in Eq. (22.14)] is often called the shock impetknce of a material. It increases very slowly with increasing pressure, but over the pressure ranges of general interest (in shock initiation) it can be considered to be nearly constant. Because of this, many workers in the explosives field combine this value into the critical energy fluence and use the term instead as the critical value for initiation. 

The critical energy fluence is a necessary condition for shock initiation of detonation, but is not, by itself, sufficient to describe the whole process in engi-... 

We have seen now that both critical energy fluence as well as pulse duration and magnitude are necessary conditions for shock initiation of detonation, but this is still not sufficient. One additional parameter must be taken into account, and that is the impact shock diameter. 

As you will recall, there must be sufficiently high-energy fluence or P t) and high enough pressure such that the explosive can be initiated in a reasonably short distance from a shock wave input. Electrical constraints limit the practical size (pressure, temperature, time) of the shock obtainable from the bridgewire, and these are such that we require an explosive with very low critical energy fluence, Ec (or and short run distance. PETN, at low density and small... 

As stated earlier, the critical energy fluence, Eq (or P t rid, must be exceeded to detonate an explosive from a shock wave. The pressure of the shock wave as well as its duration from a bursting bridgewire are functions of the burst current (or of the peak burst power). There is a minimum burst current below which we cannot detonate the initial pressing. This minimum burst current is dependent not only on bridgewire parameters, but also upon the properties of the explosive used for the initial pressing. The critical properties of the explosive that affect minimum burst current are those that affect Ec, namely, the density, particle size, and specific surface area of the particles. 

Figure 7.6 Influence of spot size on critical energy fluence to ignition MTV [14].

In accordance with eqn (2.74), a minimum energy fluence at the ionization stage is required in the schemes that make use of those resonance transitions from the excited state upward for which the ionization cross section is a maximum. With the proper choice of the sequence of transitions and intermediate quantum states, it is possible to attain a situation where all of the cross sections of the successive transitions lie in the region ai, a2,... > 10 cm and the critical energy fluences of the pulses are rather low - - < 10 —10 J/cm or < 10 -10 photons/cm. The direct... 

Equation (1.2) is at the core of the MALDI process. If a matrix is chosen with a sufficiently high absorption coefficient a, a relatively low fluence Ho suffices for achieving the critical energy density necessary to initiahze ablation and ionization of a top layer of the sample. Values for Hq of 50-500 J m are representative for most UV-MALDI applications. 

The values of t (i.e., the critical exponent for electrical conductivity versus fluence), obtained from the slope of logftr) versus log(4> - j) linear dependences for various ion-implanted polymers (polyacrylonitrile [11], polyimide [87], poly-2,6-dimethyl-polyphenyleneoxide [11], perylene derivatives [12]), are 4-5 when the energy is deposited predominantly by the collisional mechanism and 7-8 when electronic stopping prevails. These values of the critical exponent for conductivity are substantially higher than those observed for metal nanoparticles in a dielectric matrix [88], which can be apparently explained by the effects of the conducting phase ordering during the implantation. 

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