The 9th Symposium on Accelerator &ience and Technology, Tsukuba, Japan 1993

Analysis of the HIMAC Synchrotron Power Supply
M. Kumada, K. Sato, K. Noda, E. Takada, A. Itano, M. Kanazawa, M. Sudou,
National Institute of Radiological Sciences,4-9-1, Anagawa, Inage-ku, Chiba, 263, JapanS. Matsumoto, Dokkyo University, Medical School,S. Koseki, and H. Kubo, Hitachi Ltd.
Abstract
The analysis for lattice magnet power supplies of theHIMAC synchrotron is presented. The analysis showed us anadvantage of our novel features such as common mode filter,a separation of an upper and lower coil of the load and bypass
resistor across the magnet .

I. INTRODUCfiON
The design rationale of the HIMAC synchrotron system isdescribed in previous papers [1], [2], where an example of
the analysis of the electric characteristics of the power supply
and the magnets , an importance of the equivalent circuit of
6-terminal, a separation of common and normal mode and aseparation of magnet coil is particularly emphasized. In thisarticle we present more detailed study of a static filter, animpedance , an admittance , a voltage, and current of theload magnets, in presence of parallel resistors.
In our design rationale, we have introduced an idea of thedifference and the sum of the current and voltage. In thisarticle we call those components common mode and normal
mode respectively and corresponding impedance andadmittance are defined accordingly.
Common mode filter of the HIMAC is the world firsttrial to high power synchrotron magnet. An idea of damping
transient spikes by bypass resistor across the magnet by one of
the author, K. Sato, has been circulated among an accelerator
community and its effectiveness is confirmed in KEK PS
and INS TARN II. In this article , the effect of the bypass
resistor is analyzed and is shown to be effective as
experimentally and intuitively expected. By separating theexcitation coil of the dipole magnet into upper and lower weare able to shift the resonant frequency of the common mode
to higher region where filtering effect by common mode filter
is more effective. The separation of the coils also enables us
to transpose the coils among the magnet strings [1],[2].
~No.I

No.2~_.

111111II

III IIIcircuits of a conventional one and ours are compared in Fig. Ia and b. In either case of the equivalent circuit a leakage
capacitor has to be included for a study of resonant
characteristics of the magnet strings. In conventional circuit,leakage current through the leakage capacitor flows into avirtual ground line. With the virtual ground line, theequivalent circuit forms the 6 terminal circuit even in theconventional circuit. In most conventional cases, seen from apower supply side, when we number the magnet from 1 toN,
the nearest magnet is 1 and N. With the presence of theleakage capacitor, ac coupling between the number 1 and N
is inevitable. This ac coupling causes an imbalance of
current between the magnet n and magnet N-n. In addition
due to the cascade connection of the magnet, which we callmagnet strings, a magnitude and a phase of the current also
depend upon a position n of the cell. Thus one must solve the6 terminal equivalent circuit. Due to an ambiguity of theground line, however, the validity of any model of theconventional configuration is unfounded. On the other hand,in our circuit where we have added the actual third neutralline to both the power supply circuit and the load magnet
strings, the validity of our 6 terminal model depicted in Fig.lb is more reliable. The nearest magnet to the power supply
side in this scheme is the upper coil and the lower coil ofmagnet number N. With a combination of the common mode
lowpass filter and the separation of upper and lower excitationcoil, ripple component and transient spikes are expected to besuppressed.
To make a discussion simple without a loss of generality,
we assume that the upper half and the lower half of the 6terminal circuit is symmetrically made. In this case, it can beshown that the 6 terminal circuit is decoupled to two
independent 4 terminal circuit of common and normal mode
circuit.

~

No.I up~

1f~nt-n n--t
No.N~Niower

No.N·lNo. (N-1) low~

JN
Fig. I a An equivalent circuit of a conventional load

Fig. I b An equivalent circuit of HIMAC dipole load

II. CIRCUIT MODEL
In order to understand a characteristic feature of our 6terminal circuit with neutral line, simplified equivalent

In the following , an analysis is performed for decoupledcommon and normal mode circuit-211-

III. ANALYSIS

B. MAGNET STRINGS

A. STATIC FILTER
Static filter comprises of two stage common mode andnormal mode filter. In a conventional filter, only a normal
mode (summed) component is filtered; a transfer function ofoutput to input voltage of normal mode is , without a load,

For simplified symmetric 1t type model as in Fig.1 b, thetransfer matrix for normal (sum) and common (difference)mode is expressed by( U2±V2)= M(Ut±Vt)
12±12/t±lt
Z.,c1+Z.,cU2+ V2
1Ut+ Vt = 1+ZY')(Ut±Vt)

whereas transfer function of common mode is=( (2 + Z.,cYc)Z.,cYc 1+ Z.,cYc /1 ± Jt .
x,.,cZ.,c)(Ut±Vt)(= Z.,c- (1+X,.,c)(l-X,.,c) X,.,c ft±Jt

U2-V2= 1
ZY Ut+Vt
Ut- Vt
1+ZY Ut- Vt

w here Xn, c1express a measure of deviation from a resonant frequency ofa unit 1t cell and to manipulate the multiplied matrix simple.
It is also convenient to express the cell of the matrix by ahyperbolic sinusoidal function,

11+2pLY'

1+VZ-kpLY

U2+ V2
Ut+Vt

1= 1+YZ+kpLY=1.

=(MThe filter has to be evaluated with its load connected.
Our common mode filter has a bridge resistor between thecenter tap and the end of the inductor. The decoupled 4teminal transfer matrix for common and normal mode
component is,( U2-V2)
12-12

Zl

1+ Zl

= +ZJ'J(1 + ---z;-)1+Z.(l+~)1+Zl
YJ1+-z( U2+ V2)
12+12

1+Z.Y.nun(1+~) Z.(l+~)
Zl=1+ ZcY.nun(l + ----z;)1+Zly,_1

Ic(n) = Yc0 Vc(O) sinh n~
Z.:(n) = Zca cotanh n~

V0 (n) = Z..O I,.o(O) sinh n~
Yn(n) = Y nO cotanh n~la(n) = Ino(O) cosh n~
Zo(n) =Zoo tanh n~

cosh12~ = (1-8X2+8X4)(1-64X2+320X4-Sl2X6+256XB)+ Zl(Ut+Vt)+Zc(l+~) li+lt '1+-1

Vc(n) = Vc(O) cosh n~
Yc(n) = Yc0 tanh n~

where we have used suffixes of c and n for common andnormal instead of the expression I - J , I + J, U - J , U + J.
The number of cells N is 13 for Dipole and 12· for
Quadrupole respectively.
For n=12 and 13 cell, matrix elements are, in terms of X,

and1+-z ..
oa.e= ..j(X..e+ 1)(X..e- 1)

A condition of I - J = 0 and U + V = 0 at the end ofmagnet strings leads to following equations for a voltage,current, admittance, impedance at n-th cell,(Ut-Vt)/t-JtZl1cosh q
Zosinh ')sinhq /Zo coshq 'with sinh~ = 4<X,.,c+ l)(X..,c-1) , coshn~n,c =Xnc,

1
1+ZcYJ(1+~) Zc(1 + ----z;)
1+-1+~Zl

In a common mode filter, this is expressed byUt-Vt.
.
=1+ Z.,cYn,cZ. 1s a convement parameter toZlZo sinh12~ = -4j X (1+2X)(1-2X)(3-4X2}(1-2X2)(1-16X2+16X4)=-Zo •1 sinh12~
4j X (1-2X)(l-X)(1+X)(l+2X)(3-4X 2)(1- 2X2)(1-16X2+ 16X4)
cosh13~

respectively where Zc, Zn is a common mode and normal
mode impedance of the corresponding filter, Zd is a bridgeresi~tor of the filter, Y r is an admittance between the cable andneutral line, Ysum is a total admittance of the filter.

~212-= X (13-364X 2+2912X4--9984X6+16640X813312X10+4096X12)

Zo sinh13~ = j (l-6X-24X2+32X3+80X4·32XS-64X6)(1 +6X-24X2-32X3+80X4+32Xs-64X 6)
z.o-t sinh13~ j (- 1+85 Xl-1204 X4+6496 X6
j-16896X8 +22784 X 10-15360X12+4096Xt4)
I,=1

In order to evaluate the effect of the bypass resistor r, weintroduce a k parameter defined as k = Clb Lm1 /r where ro0 is aresonant angular frequency of a unit cell.
The calculated common mode admittance for different kparameter are shown in Figs.2 a,b,c,d and 3 a,b where kparameters varies from 10-6 to 0.5. Note that the admittanceis normalized by a characteristic admittance. Note also thatthe characteristic admittance and the resonant angularfrequency differ for common and normal mode, Vertical axis
is a logarithm of absolute value of the admittance andhorizontal axis is angular frequency normalized by roo,. Withhigh impedance as in Fig.l a (n=l3), the lowest resonant
frequency of the common mode appears at x= ro /roo = 0.1.
This is in contrast to the normal mode admittance where it
does at x=0.2 shown in Fig.3 a (n=l3). These figures indicatethat in conventional load, the lowest significant mode at theentrance of the load is the common mode.
There is a difference of peak position near x= 1 between
that of n=l3 and n=l2 as shown in Fig.2 a and b.
The pattern of the admittance changes as the cell number
becomes smaller with decreasing number of zero's and pole's.
This indicates a transient response is dependent upon the celllocation.
The effect of the bypass resistor is evident. from Fig; 2c, dand Fig. 3 b. As is seen an amplitude of the admittance isgreatly reduced. In JflMAC , k parameter is expected to bearound 0.1 and 0.5 for common and normal mode.
Finally, we estimate a current flowing through themagnet which is given below.

10.5

-0.5
-1

-1.5
Fig.2 c Common mode admittance n=l3, k=O.l

0.5

1.21.4-0.5-1-1.5Fig.2 d Common mode admittance n=l3, k=0.5

214-1

Z(n -1) .
Z(n -1) ·V...(n)smh~"}cosh~"+--=coshnr {1- ·"'•
Z(n)"'•Z(n)"'•
Vo(O)

-2-3
lnm(n) = Z.osinh n'n {1- Z.(n -1) cosh 'n + Zn(n -1) sinh 'nl.
Fig.3 a Normal mode admittance n=13, k=I0-6
Z.(n)
Z.(n)
Io(O)
Common mode magnet voltage; and normal mode magnet
current has more poles and zeros than that of the admittanceand shows very interesting pattern.

13-1

2-1.5

1-1

1.2 1.4-24-2-3

Fig.3 b Normal mode admittance n=l3, k=0.5

V.ACKNOWLEDGEMENTS

Fig.2 a Common mode admittance n=l3, k=lo-62
1

We gratefully acknowledge the support of all the othermembers of the division of accelerator physics andengineering, research center of heavy charged particle
therapy, NIRS.

V. REFERENCES-1-2-3
Fig.2 b Common mode admittance n=l2, k=1o-6[1] M. Kumada et al., 8th Symp. Accel. Sci & Tech.,
1991,RIKEN[2] M. Kumada et al., in the proceedings of PAC 93,
Washington, D.C, USA.

-213-