ORIGINAL RESEARCH The Effects of Ferrites on Dense Plasma Focus Device: Using a Modification to the Lee Model Hadi Barati 1 • Morteza Habibi 1 Ó Springer Science+Business Media, LLC, part of Springer Nature 2019 Abstract The Lee mode code has been promoted for better simulation of the dense plasma focus (DPF) device. At the first step, the calculation of magnetic field and tube inductance was improved to include the geometry of the rods forming the cathode. At the second step, the influences of the number of the cylindrical cathodes have been investigated. Ultimately, for enhancing the current sheath dynamics in the axial acceleration phase, the effects of ferrites located near the cathodes have been studied. Simulations were performed with integrating the modified generating equations. The influences of the ferrite’s susceptibility as well as saturation field on the current waveform, the tube inductance, and the current sheath speed in the DPF axial phase have been investigated. The numerical studies showed that increasing the number of cathodes would decrease the starting time of the pinch phase. The weak ferrites presented some enhancement in the total magnetic field and the axial speed of the current sheath. Keywords Dense plasma focus (DPF) Á Lee model code Á Tube inductance Á Ferrite Introduction Although dense plasma focus (DPF) devices have been much studied since their birth at 1960s by Mather and Philippov [1, 2], most works have been focused on empirical results and emission of neutrons and fewer studies have been done on the theory and the theoretical analysis of DPFs in comparison to the experimental works. The plasma focus device is a pulsed discharge in which a magnetically compressed plasma is produced at the end its anode [3]. The knowledge of the DPF’s mechanism demanded several theoretical and empirical approaches. Several models and methods have been developed to understand the DPF operation and to interpret its outputs [4]. The Lee model is one of the most appreciable approaches that manifests its accuracy in conformity between theoretical predictions and experimental data [4–6]. In [6], this model code is fully described. This code includes electrical circuit equations coupled with plasma focus dynamics, thermodynamics and radiation equations for a Mather-type DPF machine. These behavioral equa- tions are categorized in five phases: axial phase, radial inward shock phase, radial reflected shock phase, slow compression or pinch phase, and expanded column phase. The axial phase is described by a snowplow model with an equation of motion coupled to a circuit equation. The radial inward shock phase includes four coupled equations using the slug model. Similarly, the radial reflected shock (RS) phase is modeled by four coupled equations. When the RS hits the piston, the pinch phase starts with radiations. Three coupled equations describe this phase. In the final phase, i.e. the expanded column phase, the snowplow model is used again and two coupled equations similar to the axial phase are used. In the Lee model code, a geometrically simple plasma focus configuration was chosen to derive all these equations. This machine consists of two cylindrical coaxial electrodes in which the anode is the inner electrode [6]. The Lee model was applied to analyze voltage and current traces obtained from operating conditions of a high- energy deuteron producing DPF [7]. This code was also & Morteza Habibi mortezahabibi@aut.ac.ir 1 Department of Energy Engineering and Physics, Amirkabir University of Technology, Tehran, Iran 123 Journal of Fusion Energy https://doi.org/10.1007/s10894-019-00210-y