# MeaSUREMENTS OF THE COUPLING IMPEDANCE OF

# THE SNS EXTRACTION KICKERS\*

D. Davino^†^, H. Hahn, Y.Y. Lee, BNL, Upton, NY 11973, USA

Abstract

The Spallation Neutron Source (SNS) Accumulator ring extraction system
includes 14 modules of ferrite kicker magnets with window-frame geometry
\[1\]. Among all ring components, the extraction kickers make the single
largest contribution to the coupling impedance budget. A prototype was
constructed and various design options impacting the transverse coupling
impedance have been thoroughly studied. Bench as well as system
measurements were performed to determine the benefits from an external
circuit resistance, from using different ferrites material, and from
adding a novel ferrite winding. The results presented in this paper
confirm that a resistive termination in the external circuit yields a
solution with sufficiently reduced transverse coupling impedance. In
order to determine the total contribution of all modules, an equivalent
circuit and a simple scaling law was derived from measurements of full
and half size magnets.

## 1 INtroduction

The Spallation Neutron Source (SNS) Accumulator ring extraction system
\[1\] includes 14 modules of window-frame ferrite kicker magnets pulsed
with a rise time of 200 ns. The transverse coupling impedance of the 14
extraction kickers is expected to be the largest single contribution to
the impedance budget of the SNS accumulator ring. In this paper the
bench measurements of the longitudinal and of the transverse impedance
are presented. Various options were tested, including the effect of a
resistive termination in the external circuit and that of a different
ferrite type. Since the various kickers have different apertures, a
scaling law has been used to establish the total impedance contribution
of the smaller kickers by extrapolation from the measured full size
prototype.

![](media/image1.pct){width="0.9611111111111111in" height="1.1875in"}

Figure 1: SNS extraction kicker prototype in its vessel.

The SNS extraction kicker prototype is shown in Fig. 1. In particular,
it is possible to see the high voltage feed-thru to which the PFN
circuit is connected, the eddy current stripes, and the ceramic
structure to keep the kicker assembled. The aperture dimensions are h =
246 mm in the vertical plane and w = 146 mm in the horizontal one, the
bus-bar is 0.4 m long. The ferrite bricks are 31.8 mm thick.

## 2 Experimental Results

Bench measurements on the prototype were made using the standard method
\[2\], in which a single, or a twin-wire "Lecher" line, is inserted into
the kicker. By definition, the vertical impedance is measured with the
two-wire plane perpendicular to the bus-bar plates.

### 2.1 Longitudinal Impedance

The forward transmission coefficients S~21~ of the "Device Under Test"
and of a coaxial reference line is interpreted according to

![](media/image2.pct) (1)

with Z~L~ the characteristic impedance of the coaxial line.

As shown in Fig. 2, the value of the impedance is Z~\|\|~/n=0.3+j2.5 Ω
at 10 MHz. Copper stripes (eddy current stripes) are placed at the
middle plane of the side ferrite bricks to break the longitudinally
induced flux through the ferrite. The copper stripes reduce both,
longitudinal impedance and induced ferrite heating. Indeed, Fig. 2 shows
the increase of impedance when those eddy current stripes are removed.

![](media/image3.pct){width="3.25in" height="2.441666666666667in"}

Figure 2: Longitudinal impedance. The dashed curve is the impedance
without the eddy current stripes.

### 2.2 Vertical transverse impedance

In analogy to the longitudinal measurement, the transverse impedance
follows from:

![](media/image4.pct) (2)

with ∆ being the spacing of the two wire and ![](media/image5.pct),the
characteristic impedance of the two-wire line. The transverse coupling
impedance behavior of window frame magnets can be accurately modeled
with the equivalent circuit shown in Fig. 3.

![](media/image6.pct){width="3.248611111111111in"
height="1.3402777777777777in"}

Figure 3: Equivalent circuit for the transverse impedance.

The measured impedance,![](media/image7.pct) is "scaled" to the circuit
elements at the bus-bar through the formula

![](media/image8.pct) (3)

with the coupling coefficient κ given by the geometric ratio of the
aperture height and the wire spacing, *h/∆*.

The two elements Ls and Rs represent the impedance due to the flux which
does not couple to the external circuit, and are identified with the
measurement of the impedance with a short-circuit termination. The
elements, Lp, and Rp, represent the magnetic flux coupled with the
external circuit, whereas Cp represents local capacities, primarily that
of the bus-bar and feed-thru \[3\]. It is apparent that a resistor in
parallel with the external circuit will damp the resonance, reducing the
coupling impedance seen by the beam, as it is shown in Fig. 4. In case
of a 25 Ω termination, the peak of the open termination resonance is
damped by a factor 6. However, the resonance is shifted lower leading to
higher impedance at low frequencies (f\<10 MHz).

![](media/image9.pct){width="3.25in" height="2.441666666666667in"}

Figure 4: Vertical transverse impedance. Effect of a resistive
termination on the external circuit.

![](media/image10.pct){width="3.25in" height="2.441666666666667in"}

Figure 5: Vertical impedances with different ferrites.

It is worth noting that the external circuit is decisive for the
coupling impedance of the kicker. For the SNS case, the resistive
termination is placed in the service building and the kicker is fed
through two 90 m long coaxial cables (Z~0~= 50 Ω) in parallel connected
to the feed-thru \[4\]. Tests showed that small mismatches allow the
resonant peaks of the coaxial line to show up in the coupling impedance.
Furthermore, the 20.5 pF equivalent capacitance of the feed-thru is
responsible for a shift of the resonant frequency from about 35 MHz to
23 MHz \[5\].

The standard ferrite material used at BNL is CMD5005 \[6\]. Bench
measurements were performed on the magnet with a different type of
ferrite material, C2050, which is characterized by a lower initial
permeability, better loss factor, but a higher DC conductivity with
respect to the standard material.

For the low-μ ferrite, the resonance peak of the open termination case
is reduced by almost a factor 2, which seems in contrast with the better
loss factor property, but which can be explained by a sheared
permeability due to the air-gap \[8\]. This fact points to the
possibility of resonance damping for open-terminated kickers, but with a
25 Ω resistive termination the impedance is unchanged, as it is shown in
Fig. 5.

### 2.3 Scaling law

The extraction system of the SNS ring has 14 kickers and the their
apertures are adjusted with the betatron function to yield the overall
SNS ring acceptance (480π) \[7\]. Therefore, a scaling law is needed to
predict the impedance budget for all of the 14 kickers. Following the
reasoning that led to the equivalent circuit of Fig.3, one can write:

![](media/image11.pct) (4)

namely the product of the impedance with the square of the aperture
height is constant.

In order to verify this law, a half-size model was assembled with the
existing ferrite bricks and a new simplified bus-bar and a factor 4 was
expected. The results of the measurements are shown in Fig. 6. The
agreement is very good for the resonance peak (15% error) and for the
real part of the 25Ω termination at low frequencies. The imaginary parts
are different, as well as the resonant frequency, because of the changed
half magnet inductance and bus bar.

![](media/image12.pct){width="3.25in" height="2.441666666666667in"}

Figure 6: Scaling law verification.

### 2.4 Displaced transverse coupling impedance

In the SNS ring kickers the beam closed orbit is not centered with
respect to the geometrical kicker center, in order to reduce the kicker
aperture when the beam is deflected \[1\]. Thus, it is important to make
bench measurements with a displaced two-wire line, to check the effect
on the transverse impedance. Fig. 7 shows the case when the line is
displaced by 25.4 mm with respect to the geometrical center. The
differences in the impedance resonance peak are about 15%.

![](media/image13.pct){width="3.25in" height="2.441666666666667in"}

Figure 7: Displaced (25.4 mm) coupling impedance. Ferrite blocks are
C2050 type.

### 2.5 Ferrite winding measurements

Numerical analysis of a novel wide conductor winding around the ferrite,
behind the kicker bus-bar, suggested a significant reduction of the
kicker transverse and longitudinal coupling impedances \[9\].
Experimental verification has been performed on the kicker prototype
both for the case of 25 Ω and open termination. A clear reduction of the
impedances was obtained only above 32 MHz \[5\]. This allowed the
conclusion that the effectiveness of using a ferrite winding loop is not
obvious, at least not in the present realization, and that more
engineering studies will be needed to realize the promises and potential
advantages of this idea and to arrive at an optimized kicker design.

### 2.6 Horizontal coupling impedance

The horizontal transverse coupling impedance of the kicker is shown in
Fig. 8. This impedance is not of concern for the impedance budget. Its
contribution to the real part is negligible up to f= 30 MHz and the
almost constant imaginary part is due to the inductive behavior of the
magnet.

![](media/image14.pct){width="3.25in" height="2.441666666666667in"}

Figure 8: Horizontal transverse impedance.

## 3 ACKNOWLEDGEMENTS

The authors would like to thank Chen-Ih Pai for mechanical engineering
contributions and the Beam Components Group and the Pulsed Power Group
of the Collider-Accelerator Department for technical support.

## 4 References

\[1\] N. Tsoupas, M. Blaskiewicz, Y.Y. Lee, et al. "Beam Extraction from
the SNS Ring and Design of Extraction Kickers", EPAC'00, Vienna, June
2000, p. 2270.

\[2\] F. Caspers, in Handbook of Accelerator Physics and Engineering,
ed. A.W. Chao and M. Tigner, (World Scientific, Singapore, 1998), p.
571.

\[3\] D. Davino, H. Hahn, in preparation.

\[4\] Jian-Li Mi et al., these proceedings.

\[5\] D. Davino, H. Hahn, "Measurements and analysis of the transverse
coupling impedance of the SNS extraction kickers", BNL/SNS Tech. Note
No. 102, BNL, (2001).

<http://server.ags.bnl.gov/bnlags/bnlsns/102.pdf>

\[6\] Ceramic Magnetics inc., Fairfield, NJ, USA.

\[7\] J. Wei et al, Phys. Rev. ST-AB 3, 080101 (2000).

\[8\] H. Hahn, D. Davino, these proceedings.

\[9\] S.S. Kurennoy, D. Davino, Y.Y. Lee, "Reducing beam coupling
impedances in SNS ring extraction kickers", PAC'01, Chicago, June 2001.