Lecture 2. Diagnostic equipment of the TEMP-4M accelerator The TEMP-4M Ion beam generator construction Diagnostic equipment of the TEMP-4M accelerator. Calibration of diagnostic equipment. Energy transfer efficiency in the accelerator (Marx generator, pulse forming line, diode). http://portal.main.tpu.ru:7777/SHARED/a/AIPUSH

Blumline Marx Rogowski coils for Blumline, main spark gap and diode Voltage divider Low inductive shunt 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. 3531-3535 2 2

Rogowski coil I0 load 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 I0(t).

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

Schematic circuit of RC load When the condition ωRнС << 1 is fulfilled the influence of parasitic capacitance is negligible Then from Kirchhoff equation we find: Irc E(t) - electromotive force IRC – measured current 5

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: F=BS Magnetic induction B at a distance r from an infinitely long straight current-carrying conductor is given by (Biot-Savart law) r load where I0 - the measured current.

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

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

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

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

IRC I0 R R load

I0 = 50 kA I0 = 50 kA R = 10 Ohm N = 500 U = 1 kV

IRC I0 load М – magnetic coupling coefficient

In case of (1) =0 A so called mode of “impact excitation circuit” is realized from Eq. 1: In this case measured current equals: IRC I0 14

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

Rowoski coil with a reverse coil

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, 053106 (2011)

M. Matsuda, D. Wang, T. Matsumoto, T. Namihira, and H 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. 19

Impact excitation circuit The Mercury ion diode, showing locations of current monitors 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. 227.

B(t) = ? Impact excitation circuit 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)

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

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

Three Level voltage divider Marx Na2S2O35H2O solution Na2S2O35H2O solution

MARX

Capacitive voltage divider С1 С2 К= C2/C1

Equivalent circuit of the voltage divider C, С1 - 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; UR - voltage at the differential divider output. 27

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 107 Hz. 28

A Differential High Voltage Divider Voltage pulse rise time is less than 5 ns, so the maximum frequency of harmonics is equal to 2 × 108 Hz. When resistance of capacitor C2 exceeding wave impedance of cable more than 10 times, the influence of the capacitance of Differential voltage divider is negligible. This is accomplished by Isakova Yu., Pushkarev A. and Kholodnaya G. A Differential High-Voltage Divider // Instruments and Experimental Techniques, 2011, Vol. 54, No. 2, pp. 183–186. 29

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

In the opposite case when the condition 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) = UR(t). In the opposite case when the condition 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. 31

Pulsed electron accelerator TEU-500 TESTING OF THE VOLTAGE DIVIDER Pulsed electron accelerator TEU-500

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 33

Measurement of Marx charging voltage (in water)

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*Rshunt Rshunt = 0,0485 Ohm

Lecture 1. TEMP-4M accelerator The TEMP-4M Ion beam generator construction Diagnostic equipment of the TEMP-4M accelerator Calibration of diagnostic equipment. Energy transfer efficiency in the accelerator (Marx generator, pulse forming line, diode). http://portal.main.tpu.ru:7777/SHARED/a/AIPUSH

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

Calibration of Rogowski coil at the output of DFL Active load R=5.2 Ohm, L=240 nH KRC = 200-300 A/B Waveforms of signals from RC at the output of DFL and from shunt

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

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

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

Calibration of diagnostics at the output of Marx Blumline Marx 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) Charging voltage of DFL can be calculated as: C=?

Calculation of capacitance of DFL Blumline C=? Schematic of DFL of TEMP-4M accelerator For calculation of DFL capacitance we use a formula for capacitance of a cylindrical capacitor Сcalc Сexp, nF ρ by charge by period Inner forming line 14.1 nF 14 ±0.3 14 ±0.1 2.5 Ohm Outer forming line 17.3 nF 16.5±0.2 16.7±0.1 2.2 Ohm

Blumline 45

The capacitance of forming line can be determined experimentally from the analysis of transients during charging of DFL Blumline 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) Kumar D., Mitra S., Senthil K. et al.// Review of Scientific Instruments, v.78, 115107 2007

Сavr = 16.5 nF Current oscillations in the series resonant circuit is: Zernov N.V,. Karpov V.G. Theory of radio circuits - Moscow-Leningrad .: Energy, 1965 - 892 p.

C2 = 16.5 nF before breakdown of output spark gap (t <0.5 mks) 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) C2 = 16.5 nF before breakdown of output spark gap (t <0.5 mks) and C2 = 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)

Calculation of capacitance of DFL Blumline C=? Schematic of DFL of TEMP-4M accelerator For calculation of DFL capacitance we use a formula for capacitance of a cylindrical capacitor Сcalc Сexp, nF ρ by charge by period Inner forming line 14.1 nF 14 ±0.3 14 ±0.1 2.5 Ohm Outer forming line 17.3 nF 16.5±0.2 16.7±0.1 2.2 Ohm

Ucalc=R·I+(L1+L2)∙dI/dt Calibration of diagnostics with the accelerator running on resistive mode Ucalc=R·I+(L1+L2)∙dI/dt Voktage was calculated using the formula: Kalantarov et al. Book of Inductance calculation.1986