# Assessment of the Sympathetic Detonation of Blasting Caps
## 1 Introduction
[7] investigated experimentally and numerically the shock sensitivity of a shaped charge underwater and showed that in an underwater explosion, the index of the sympathetic detonation is slightly higher than in the air. Along with the previously mentioned research teams, several others can easily be named, including researchers/teams that approached the subject in a theoretical manner, such as [PERSON], [PERSON], [PERSON], and [PERSON] [6, 8, 9, 10]. When an explosive charge (explosive bars) is subjected to the action of a shock wave, this shock wave will produce the initiation of the acceptor charge only if the energy of the shock wave is greater than the critical energy. The critical energy considers not only the pressure level (shock amplitude) but also the pulse duration and the acceptor impedance as stated by [PERSON] and [PERSON] [11]. The formula for energy calculation is given in Equation (1). \[E_{c}=P^{2}t/\rho_{0}U \tag{1}\]  
where \(P\) is the shock amplitude, \(t\) indicates the pulse duration, \(\rho_{0}\) denotes the acceptor's initial density, and \(U\) is the shock velocity that travels through the acceptor. The term \(E_{c}\) has the dimension of energy per unit area and is therefore referred to as energy fluence. Through experimental tests carried out with different explosives subjected to the square-wave shock produced by the impact of the flyer test, it was found that each explosive has a range of energy fluence in which a stable detonation is produced, called critical energy fluence [12]. Additionally, for the evaluation of the initiation of an explosive under the action of the shock wave, the \"Pop-plot\" [12] can be considered, which represents the graphic representation in logarithmic coordinates of the run distance as a function of pressure for the acceptor explosive. The application of Equation (1) used to evaluate the initiation of detonation of an explosive charge requires the determination, by numerical analysis, of the amplitude and duration of the applied shock. In the absence of numerical analysis, the relationship developed by [PERSON] [13] takes into account detonation parameters, which are easier to measure and can be used to determine the energy transmitted to the explosive charge. This relation is specified in Equation (2). \[E_{c}=\frac{\rho_{0}D_{j}\delta\left[\frac{D_{j}-a_{x}}{2b_{x}}+\frac{D_{j}}{2(r+1) }\right]^{2}}{D_{j}-\left[\frac{D_{j}-a_{x}}{2b_{x}}+\frac{D_{j}}{2(r+1)}\right]} \tag{2}\]  
where \(\rho_{0}\) is the initial density, \(D_{j}\) is the velocity of detonation, \(\delta\) is the thickness of reaction, \(r\) denotes the specific heat ratio of detonation products, and \(a_{x}\) and \(b_{x}\) are Hugoniot constants. In line with the sympathetic detonation issue, yet in a less conventional manner, the current paper focuses on the investigation of the sympathetic detonation tendency of the blasting cap, containing pentaerythnitol tetranitrate (PETN) charges. The main focus is targeted on investigating the applicability of critical energy fluence for a particular configuration with an air gap between donor and acceptor explosive charges. For the assessment of the detonation initiation potential of a blasting cap, in this paper, we will use Equation (1) because, when using numerical analysis, the parameters in this equation are determined much faster. The relevance of the study is obvious when one considers the specific way in which the neutralization of suspicious packages is carried out. Basically, the disruption of such packages is performed by propelling a disrupting agent (metallic/plastic bolts or water) with the use of small explosive charges. The blast wave generated by the detonation of an explosive charge has the potential, in certain conditions, to lead to unwanted package detonation due to the initiation of explosive charge and/or blasting caps.