International Journal of Pure and Applied Mathematics Volume 114 No. 7 2017, 531-546 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu Special Issue ijpam.eu Serial Step Up Resonant Frequency Static Discharge System - Tesla Gun R. Ramya1, Abhinash Kumar Patra2, Saurodeep Adhikary3, Rishav Ranjan Paul4 SRM University, Kattankulathur [email protected] and [email protected] Abstract Currently weapons research and development takes up the greatest share of any defense budget. In this aspect, India is lagging, mostly due to economical and institutional constraints. It is the largest importer of arms and ammunitions in the world. However, there is still a need for a failsafe defense system. This paper is a step towards addressing this shortcoming of the Indian military. However, this is not the first prototypal weapons system in the world. The U.S. Defense Strategic Defense Initiative put into development the technology of a similar type using a particle beam to be used as a weapon in outer space as part of the Beam Experiments Aboard Rocket (BEAR) project. This is the next step to build a weapon system that rises above ammunition constraint and environmental hazard. The basic premise of a Tesla Gun involves static discharge at a very high voltage. There are three main elements of the system. The first is the voltage step up. The next is the resonant circuit and the final element is the targeting system. Key Words and Phrases: Tesla Coil, Static Discharge, Resonant Frequency, Bounces. 1. Introduction 1 531 International Journal of Pure and Applied Mathematics Special Issue A Tesla coil is a device producing a high frequency current, at a very high voltage but of relatively small intensity. Basically, it works as a transformer and as a radio antenna, even if it differs radically from both. A Tesla coil is a radio frequency oscillator that drives an air-core double-tuned resonant transformer to produce high voltages at low currents. Tesla's original circuits as well as most modern coils use a simple spark gap to excite oscillations in the tuned transformer. More sophisticated designs use transistor or thyristor switches or vacuum tube electronic oscillators to drive the resonant transformer [1]. Tesla coils can produce output voltages from 50 kilovolts to several million volts for large coils. The alternating current output is in the low radio frequency range, usually between 50 KHz and 1 MHz. Although some oscillator-driven coils generate a continuous alternating current, most Tesla coils have a pulsed output; the high voltage consists of a rapid string of pulses of radio frequency alternating current. The common spark-excited Tesla coil circuit consists of these components: A high voltage supply transformer (T), to step the AC mains voltage up to a high enough voltage to jump the spark gap. Typical voltages are between 5 and 30 kilovolts (kV). A capacitor (C1) that forms a tuned circuit with the primary winding L1 of the Tesla transformer. A spark gap (SG) that acts as a switch in the primary circuit. The Tesla coil (L1, L2), an air-core double-tuned resonant transformer, which generates the high output voltage. Optionally, a capacitive electrode (top load) (E) in the form of a smooth metal sphere or torus attached to the secondary terminal of the coil. Its large surface area suppresses premature corona discharge and streamer arcs, increasing the Q factor and output voltage. Figure 1: Basic Tesla Coil Circuit 2 532 International Journal of Pure and Applied Mathematics Special Issue 2. Simulations for system parameter 2.1 Software used JAVATC by Barton B. Anderson TESLAMAP 2.2 Spark size The spark size is directly dependent on the input power from the NST. An approximate value of the spark can be derived using (1) (2) where L is the spark length and P is the input power. Input Arc Length P Voltage Inches Cm 10 13.04 6.13 15.60 20 26.09 8.68 22.06 30 10.63 10.63 27.02 40 52.17 12.28 31.20 50 65.22 13.73 34.89 60 78.26 15.04 38.22 70 91.30 16.24 41.28 80 104.35 17.37 44.13 90 117.39 18.42 46.81 100 130.43 19.42 49.34 230 300 29.44 74.82 Table 1: Correlation of input power and arc length 2.3 Primary inductance The inductance is necessary for the calculation of the resonant frequency. The primary inductance is determined from the primary coil as the other components have negligible inductances. The system has been designed to provide tuning options used taps in the primary coil. It is found using (3) 3 533 International Journal of Pure and Applied Mathematics Special Issue (4) Where L is the inductance, N is the number of turns, A is the area of conductor, D1 is the internal diameter, W is the wire diameter and S is the wire spacing. S = 7.7917 mm, W = 12 mm, D = 165 mm, D0 max = 640 mm Turns Inductance 11 44.434 11.25 46.801 11.5 49.247 11.75 51.772 12 54.378 Table 2: Variation in inductance 2.4 Resonant frequency The resonant frequency dictates the capacitor charging rate and thus the capacitor used. It is also instrumental in the operation of the coil as a gun. The resonant frequency is calculated from the primary circuit inductance and capacitance. (5) where L is the inductance, C is the capacitance and F is the resonant frequency. L C F 44.43 11.11 226.519 46.801 11.11 220.717 49.247 11.11 215.165 54.378 11.11 204.763 Table 3: Resonant frequency computation 3. Prototype of Tesla Gun 3.1 Charging system The first stage is the voltage step. The supply is from a DC battery source or from the AC mains (230 V-1ph, 415 V-3ph). In the case of DC source, a fly-back transformer is used to convert low voltage of 18 V to high voltage of more than 20 kV. In case of AC source, a High Voltage Transformer used. The components of the charging system are: 4 534 International Journal of Pure and Applied Mathematics Special Issue A. Neon Sign Transformer The high voltage transformer is the most important part of the system. It is simply an induction transformer which acts as the power supply of the system. Its role is to charge the primary capacitor at the beginning of each cycle. Apart from its power, its ruggedness is very important as it must withstand terrific operation conditions. The widely-used type of transformer is the neon sign transformer (NST), which is, as its name suggests, generally used to power neon signs. They generally supply between 6 and 15 kV and are current-limited often at 30 or 60 mA. They are safer and easier to find but are more fragile. But newer NST should be avoided, as they are provided with a built-in differential circuit breaker, which will prevent any Tesla gun operation as it provokes repeated spikes of current and voltages that will trigger the breaker. Beside from these two common types, one can also use a fly back transformer or a microwave oven transformer (MOT). In the case of this system the NST used has the following specifications: Output Voltage (V) = 10 kV Maximum Current (I) = 30 mA Also, important to computations is the power and impedance. Power (P) = V × I = 300 W Impedance (Z) = V/I = 333.33 kΩ B. Capacitor bank Energy stored in the capacitor is given by: The output from the transformer is used to charge the capacitor bank. The benefit of using a capacitor bank is instantaneous current release for the spark gap. This discharge goes to the primary coil. Its capacitance must be such as there is resonant amplification in the primary circuit (LC circuit in series with an alternating voltage generator). The capacitance is Cres. If the capacitance is lower than Cres the energy available for the rest of the cycle will be lower. The same thing would happen if the capacitance is larger than Cres, but the larger capacitance allows more charge to be stored, which 5 535 International Journal of Pure and Applied Mathematics Special Issue compensates the first problem. But due to resonance that it might be judicious to make a "bigger" capacitor in order to prevent the amplification from becoming too powerful, which could easily destroy the transformer as well as the capacitor. By definition, Cres could be found with the resonant frequency formula for 50 Hz, but the total inductance of the primary circuit should be known. It is important to note that the inductance of the transformer is much greater than the inductance of the primary coil, and the same is true for their impedances. Therefore, the primary inductor's contribution is neglected. The aforementioned formula is the following: -1 Cres = (2 × π × Z × f) = 9.54 nF The specifications of the Alcon FF – 06 are as follows: Capacitance 100 nF DC Voltage Tolerance 2000 V Maximum pulse rise time (dV/ dt) 1500 V/µs Dissipation factor (Tan δ) 0.01 kHz at 25 C Temperature Range -25 C to 85 C Table 4: Capacitor specifications The notion of dV/dt represents the speed at which a capacitor is charged or discharges (its units are V/s). In this context, it is not really the time-derivative of the potential but rather the maximal value it can take.