Lecture 14. Diagnostic equipment of the accelerators 1. Diagnostic equipment of the TEMP-4M accelerator 1.1. Rogowski coil 1.2. Voltage divider 1.3. Low inductive shunt http://portal.main.tpu.ru:7777/SHARED/a/AIPUSH

Diagnostic equipment of the TEMP-4M accelerator ПР3 Схема ускорителя: 1, 4 – газовые разрядники; 2, 5 – делители напряжения; 3 – ДФЛ; 6 – пояс Роговского; 7 – магнитоизолированный диод; 8 – вакуумная камера; 9 – мишенный узел; 10 – вакуумная система; 11- генератор импульсных напряжений (ГИН); 12 – система газоподачи и водоподготовки

I0 1.1. Rogowski coil Diagnostic equipment of the TEMP-4M accelerator Rogowski coil is used for measuring 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 1.1. Rogowski coil Schematic circuit of RC E(t) – electromotive force

Schematic circuit of RC 1.1. Rogowski coil Schematic circuit of RC C 0 When the condition ωRнС << 1 is fulfilled the influence of parasitic capacitance is negligible Then from Kirchhoff equation №1 we find: Irc E(t) - electromotive force IRC – measured current 5

1.1. Rogowski coil 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 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) D d where I0 - the measured current.

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

Formula for calculation of inductance of a toroidal coil 1.1. Rogowski coil D d Formula for calculation of inductance of a toroidal coil Kalantarov et al. Inductance calculation.1986

1.1. Rogowski coil 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:

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

1.1. Rogowski coil IRC I0

1.1. Rogowski coil I0 = 50 kA I0 = 50 kA R = 10 Ohm N = 500 U = 1 kV

1.1. Rogowski coil IRC I0 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

1.1. Rogowski coil 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.

1.1. Rogowski coil ПР3 16

Rowoski coil with a reverse coil 1.1. Rogowski coil Rowoski coil with a reverse coil

1.1. Rogowski 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)

1.1. Rogowski coil 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

1.1. Rogowski coil 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) = ? 1.1. Rogowski coil 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. 1.1. Rogowski coil 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 ПР3 Distribution of magnetic induction in cross section of diode.

1.1. Rogowski coil Magnetic field measurement on A-C gap of the diode with magnetic self-isolation N - number of coils S – area of coil

Lecture 14. Diagnostic equipment of the TEMP-4M accelerator 1.1. Rogowski coil 1.2. Voltage divider 1.3. Low inductive shunt http://portal.main.tpu.ru:7777/SHARED/a/AIPUSH

1.2. Voltage divider MARX

1.2. Voltage divider 1.2. Voltage divider Na2S2O35H2O solution

Импульсный электронный ускоритель ТЭУ-500 1.2. Voltage divider Импульсный электронный ускоритель ТЭУ-500

1.2. Voltage divider 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 divider output. 29

1.2. Voltage divider 1.2. Voltage divider С С1 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: С С1 The pulse duration is 100 ns, then the minimum frequency of signal spectrum is 107 Hz. 30

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. 31

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, 32

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. 33

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

Measurement of accelerating voltage in accelerator (in vacuum) Waveforms of the voltage at the output of the differential (1) and (2) capacitive voltage dividers, and the solid line is the calculated voltage 35

Measurement of Marx charging voltage (in water)

1.2. Voltage divider 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.

Lecture 14. Diagnostic equipment of the TEMP-4M accelerator 1.1. Rogowski coil 1.2. Voltage divider 1.3. Low inductive shunt http://portal.main.tpu.ru:7777/SHARED/a/AIPUSH

1.3. Low inductive shunt To osc. U = I*Rshunt Rshunt = 0,0485 Ohm

Lecture 14. Diagnostic equipment of the TEMP-4M accelerator 1.1. Rogowski coil 1.2. Voltage divider 1.3. Low inductive shunt