Istituto di Fisica. Universita di Leece. Leece. Italy. (Received 2 October 1978; accepted for publication 5 March 1979). The theory is given of the voltage output of ...
Rogowski coils: theory and experimental results V. Nassisi and A. Luches Citation: Rev. Sci. Instrum. 50, 900 (1979); doi: 10.1063/1.1135946 View online: http://dx.doi.org/10.1063/1.1135946 View Table of Contents: http://rsi.aip.org/resource/1/RSINAK/v50/i7 Published by the American Institute of Physics.
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Rogowski coils: theory and experimental results V. Nassisi and A. Luches Istituto di Fisica. Universita di Leece. Leece. Italy (Received 2 October 1978; accepted for publication 5 March 1979)
The theory is given of the voltage output of a Rogowski coil excited by a current pulse flowing along the axis of the coil. In this theory the Rogowski coil is considered as a delay line. The results do not differ from those obtained usually by considering the coil as a voltage source d / dt with an inductive output impedance. Details are also given of the design of two Rogowski coils and their working modes are fully analyzed.
INTRODUCTION
The production of electron beams of even higher currents and lower rise times and durations requires the development of diagnostic tools able to give confident measurements. For this purpose a number of probes were designed. Frequently they were well known and broadly used probes, modified to give uniform responses even at the highest currents and frequencies.1,2 The Rogowski coiP is now widely used to monitor high-intensity relativistic electron beams. It has the advantage of measuring currents up to tens of MA with no interference on the beam and without connections to highvoltage conductors. This probe is essentially a toroidal winding of n turns of small area, linked by the magnet flux created by the current I p to be measured (Fig. I). If properly instrumented the coil is able to detect subnanosecond pulses. The output current is, when the coil is closed on a suitable load resistance R(' and is excited by a pulsed beam current of shape (1)
II' = IOl'u(f)
where u(t) = 1 for
f
> 0 and
u(t)
= 0 for
f
< 0, is
---+2. Cross section of a toroidal Rogowski coil contained in a metallic shield. FIG.
of the working mode of the Rogowski coil, considered as a delay line. I. THEORY
Generally the Rogowski coil is contained in a metallic box which shields it from undesirable stray fields. A slit around the inside of the shield prevents shorting of the secondary winding (Fig. 2). The electric diagram of the coil closed into its metallic shield is outlined in Fig. 3. Let us now call IZ I and I y I the impedance and admittance per unit length, respectively. The equations which govern the voltage and current transmission along the line are av(x ,f)
-Izli(x,t) - fU),
ax
where n is the number of turns of the coil. 4 This result does not take into account the distributed capacitance along the coil which lets it behave like a delay line and limits the transmission speed of any signal along the coil. In the next section we will give a more general treatment
(3)
ai(x ,f)
--- = -
I y Iv(x,1),
ax
where v(x ,f) is the voltage and i(x ,f) is the current along the line. Let us now consider the line shorted at x = I, where I is the length of the toroidal coil, and terminated
L
R
f (n
L(x.n - -
G C -
L(X,t)
x Schematic diagram ofa Rogowski coil.lp-primary current (electron beam current), i.,-secondary current (induced current); B-magnetic field; R-load resistance. FIG.
900
I.
Rev. Sci. Instrum. 50(7), Jul. 1979
FIG. 3. Electric diagram of a Rogowski coil closed into its metallic shield. G, C. L. R, and 1(1) are the conductance. capacitance. inductance. resistance. and inducted voltage per unit length. respectively.
0034-6748/79/070900-03$00.60
© 1979 American Institute of Physics
Downloaded 26 Oct 2012 to 192.84.152.244. Redistribution subject to AIP license or copyright; see http://rsi.aip.org/about/rights_and_permissions
900
gas
~
probe
IHb~¥~'~
10V
I
FIG. 4. Schematic diagram of the coaxial calibration fixture, showing the high-voltage coaxial pulser, probe, and matching resistors. FIG. 6.
with resistance Re at x = O. If the line is excited by a current pulse of shape Ip = Iopu(t), the system (3) is solved by V(x,p) I(x,p)
=
=
e Yo.r - e Yo(21-.rJ IopReRo 1 + ()e 2Yo[ np(Rc + Ro) e Yo.r + e Yo(21-.rJ IopR,. 1 + ()e 2Yol np(R,. + Ro)
(4)
where V(x,p) and I(x,p) are the Laplace transforms of resistance of the line, () = (R,. - Ro)/(Re + Ro) is the reflection coefficient, Yo = - [Z(p )Y(p )]112 is the propagation function per unit length, Z(p) = R + pL, and As
+ pc.
le 2Y I
