1 1.The TEMP-4M Ion beam generator construction 2.Diagnostic equipment of the TEMP-4M accelerator. 3.Calibration of diagnostic equipment. 4.Energy transfer efficiency in the accelerator (Marx generator, pulse forming line, diode). Lecture 2. Diagnostic equipment of the TEMP-4M accelerator

1.Rogowski coils for Blumline, main spark gap and diode 2.Voltage divider 3.Low inductive shunt 2 Yulia I. Isakova. Diagnostic Equipment for the TEMP-4M Generator of High-current Pulsed Ion Beams // Journal of the Korean Physical Society, Vol. 59, No. 6, December 2011, pp Blumline Marx

Rogowski coil Rogowski coil is used for measuring high speed current pulses or current of charged particle beams. It consists of a closed solenoid (can be any shape) with a uniform winding. The principle of operation is based on registration of magnetic filed produced by a measured current I 0 (t). I0I0 load

4 Schematic circuit of RC E(t) – electromotive force load

5 When the condition ωR н С << 1 is fulfilled the influence of parasitic capacitance is negligible E(t) - electromotive force I RC – measured current Schematic circuit of RC C 0C 0 Then from Kirchhoff equation we find: I rc load

According to the law of electromagnetic induction, for a coil located in an alternating magnetic field, the electromotive force is equal to: where N - number of coils, F - magnetic flux through one coil. Magnetic flux is equal to the product of magnetic induction B and the magnitude of area S, perpendicular to the direction of the field: where I 0 - the measured current. Magnetic induction B at a distance r from an infinitely long straight current-carrying conductor is given by (Biot-Savart law) F=BSF=BS r load

7 For Rogowski coil with outer diameter D and diameter of wire d: D d F=BS.F=BS. load

8 D d Formula for calculation of inductance of a toroidal coil Kalantarov et al. Inductance calculation.1986 load

Formula for calculation of inductance of a toroidal coil [Kalantarov et al] For Rogowski coil with diameter D and diameter of wire d: The electromotive force in RC is then:

10 (2) (3) This mode of RC operation is called a current transformer mode Inductance of winding is μ – magnetic conductivity of core. = 0 Provided that  (1)(1)

11 I RC I0I0 R load R

I 0 = 50 kA R = 10 Ohm N = 500 U = 1 kV I 0 = 50 kA

13 М – magnetic coupling coefficient I RC I0I0 load

14 In case of A so called mode of “impact excitation circuit” is realized from Eq. 1: In this case measured current equals: (1) =0 I RC I0I0

Time constant for Rogowski coil significantly longer than the duration of the recorded current pulse (100 ns) that provides RC operation in current transformer mode without distortion of the current pulse form in the load.

16

17 Rowoski coil with a reverse coil

18 Schematic of the Mercury diode region, showing the location of the monitors for measuring the anode (total) current, cathode current, and ion current D. D. Hinshelwood et al. Ion diode performance on a positive polarity inductive voltage adder with layered magnetically insulated transmission line flow // PHYSICS OF PLASMAS 18, (2011)

19 M. Matsuda, D. Wang, T. Matsumoto, T. Namihira, and H. Akiyama // Proceedings of the 3rd Euro-Asian Pulsed Power Conference/18th International Conference on High-Power Particle Beams. Abstract Book (Korea, Jeju, 2010), p. 308.

20 D. D. Hinshelwood, et al. High-Voltage, High-Impedance Ion Beam Production // Proceedings of the 17th IEEE Pulsed Power Conference, Washington, DC, 2009, edited by F. Peterkin and R. Curry (IEEE CF09PPC- DVD, Piscataway, New Jersey, 2009), p The Mercury ion diode, showing locations of current monitors Impact excitation circuit

21 Diode connection for planar strip diode with self-magnetic filed: potential electrode (1), grounded electrode(2), collimated Faraday cup(3), Rogowski coil (4 и (5) B(t) = ? Impact excitation circuit

Distribution of magnetic induction in cross section of diode. Across А-C gap B(t) = 0.014·I(t), T, at current in kA I = 10 kA Distribution of magnetic field in A-C gap (Elcut) 8 mm anode cathode 40 mm 40 mm×1 mm, current 10 kA

23 N - number of coils S – area of coil Current measurement on the cathode of the diode with magnetic self-isolation

24 Three Level voltage divider solution Na 2 S 2 O 3  5H 2 O solution Na 2 S 2 O 3  5H 2 O Marx

25 MARX

С1С1 С2С2 Capacitive voltage divider К= C 2 /C 1

27 Equivalent circuit of the voltage divider C, С 1 - capacitances of the divider’s electrode cathode to the potential disk of the cathode assembly and the chamber housing, respectively; R - load resistor; U(t) - measured voltage; U R - voltage at the differential divider output.

28 It is possible to neglect the influence of the spurious capacitance value of С1 of the differential voltage divider, when the value of С1 in the parallel R–С1 chain is small. This is fulfilled on conditions that: The pulse duration is 100 ns, then the minimum frequency of signal spectrum is 10 7 Hz.

29 A Differential High Voltage Divider Isakova Yu., Pushkarev A. and Kholodnaya G. A Differential High-Voltage Divider // Instruments and Experimental Techniques, 2011, Vol. 54, No. 2, pp. 183–186. Voltage pulse rise time is less than 5 ns, so the maximum frequency of harmonics is equal to 2 × 10 8 Hz. When resistance of capacitor C 2 exceeding wave impedance of cable more than 10 times, the influence of the capacitance of Differential voltage divider is negligible. This is accomplished by

30 The voltage at the differential divider output is Therefore, the voltage at the divider output is The voltage across the divider’s capacitor is U C = U(t) – U R (t). From relation (1), we obtain the following equation: and, upon its transformation, DESIGN RELATIONSHIPS The current in the divider circuit where U С is the voltage across С

31 When the capacitance of the differential divider to the potential disk of the cathode assembly is very large, it is possible to neglect the first summand in (2), and, therefore, U(t) = U R (t). is met, from (3), we obtain the equation relating the measured voltage to the voltage recorded at the output of the differential divider: Attenuation coefficient of differential divider is K = 1/RC. In the opposite case when the condition

Pulsed electron accelerator TEU-500 TESTING OF THE VOLTAGE DIVIDER

33 Measurement of accelerating voltage in electron accelerator (in vacuum ) Waveforms of the voltage at the output (1) of the differential and (2) capacitive voltage dividers, and the solid line is the calculated voltage

Measurement of Marx charging voltage (in water)

35 Schematic of the Mercury front end and diode setup with the vacuum voltmeter mounted vertically. The torus is used to prevent electron emission at the entrance to the cylinder holding the voltmeter stack.

2.4. Low inductive shunt To osc. U = I*R shunt R shunt = 0,0485 Ohm

37 1.The TEMP-4M Ion beam generator construction 2.Diagnostic equipment of the TEMP-4M accelerator 3.Calibration of diagnostic equipment. 4.Energy transfer efficiency in the accelerator (Marx generator, pulse forming line, diode). Lecture 1. TEMP-4M accelerator

Block diagram of the accelerator: 1 – Marx generator; 2 – double forming line (DFL), 3 – diode chamber, 4 – load. 3. Calibration of diagnostics 38 Blumline Marx

Waveforms of signals from RC at the output of DFL and from shunt Active load R=5.2 Ohm, L=240 nH Calibration of Rogowski coil at the output of DFL 39 K RC = A/B

Внешний вид пояса Роговского Calibration of Rogowski coil at the output of Marx 40 Blumline

41 Calibration of voltage divider attenuator Voltage divider of DFL Osc. Pulsed generator

42 Waveforms of voltage at the input and output of DFL К = 1050 ± 1%

Calibration of diagnostics at the output of Marx Charging voltage of DFL can be calculated as: Waveforms of DFL charging voltage (1, points) and charging current DFL (2) and calculated values of voltage at С=14 nF (3) and 24 nF (4) 43 C=? Blumline Marx

44 Calculation of capacitance of DFL С calc С exp, nF ρ by chargeby period Inner forming line 14.1 nF14 ±0.314 ± Ohm Outer forming line 17.3 nF16.5± ± Ohm For calculation of DFL capacitance we use a formula for capacitance of a cylindrical capacitor Schematic of DFL of TEMP-4M accelerator C=? Blumline

45 Blumline

46 The capacitance of forming line can be determined experimentally from the analysis of transients during charging of DFL Kumar D., Mitra S., Senthil K. et al.// Review of Scientific Instruments, v.78, Equivalent circuit Marx + DFL: C1 - capacity of Marx, C2 - average capacity of DFL, L - self-inductance of Marx, R - resistive losses. Waveforms of current measured by Rogowski coil in Marx in a mode without breakdown of spark gaps (1- points) and calculated current of self-oscillations (2- line) Blumline

47 Current oscillations in the series resonant circuit is: Zernov N.V,. Karpov V.G. Theory of radio circuits - Moscow-Leningrad.: Energy, p. С avr = 16.5 nF

48 Waveforms of the current measured by a Rogowski coil of Mark in a mode without breakdown of the main spark gap (1- points), and calculated current of self- oscillations before breakdown of preliminary spark gap (2- line) and after breakdown (3 - line). Curve 4 – Rogowski coil current at the output of DFL after breakdown of spark gap (initial part) C 2 = 16.5 nF before breakdown of output spark gap (t <0.5 mks) and C 2 = 30.5 nF after breakdown output gap Pushkarev A., Isakova Yu., Zhang Xiaofu. Energy balance in double forming line in double pulse mode // (Instruments and Experimental Techniques 2015, in print)

49 Calculation of capacitance of DFL С calc С exp, nF ρ by chargeby period Inner forming line 14.1 nF14 ±0.314 ± Ohm Outer forming line 17.3 nF16.5± ± Ohm For calculation of DFL capacitance we use a formula for capacitance of a cylindrical capacitor Schematic of DFL of TEMP-4M accelerator C=? Blumline

Voktage was calculated using the formula: Calibration of diagnostics with the accelerator running on resistive mode 50 U calc =R·I+ ( L 1 +L 2 ) ∙dI/dt Kalantarov et al. Book of Inductance calculation.1986