RAYTHEON COMPANY

Microwave and Power Tube Division

Walthaw, Massachusetts 02254

OPTIMIZATION OF A MAGNET CIRCUIT DESIGN

FOR A CYLINDRICAL MASS SPECTROMETER

(NASA-CR-1764CC) OPTIBIZAiICN OF A SkGNET 1186-1`_543

CIRCUIT GZSIGN f06 A CYLINLEICAL BASS

SPECTROMETER (Raytbeon Co.) 12 p

HC A02/MF A01 CSCL 09C Unclas

G3/33 02491

Prepared for

University of Maryland

Institute of Physical Science Technology

4215 Space Park, Maryland 20742

Contract No. B252037

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25 October 1983
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1.0 INTRODUCTION

This report sun.mari;:es t esults of an optimization effort to achieve a

minimum Weight configuration fo. a magnetic section circuit (MSC) used in the

magnetic portion of a double-focusing mass spectrometer.

A prototype magnetic circuit Which had been designed and fabricated on a

previous contract was found to provide the required magnetic field uniformity.

However, the basic approach for controlling the magnetic leakage field involved

boundary matching techniques which were not efficient. Compensation magnets,

which were introduced into the magnetic circuit at the outer sector boundaries,

actually increased the total amount of magnetic flux outside the active focusing

zone. In effect, the unused portion of magnetic flux occurring in the fringing

fields external to the structure was being supplied by a major fraction of the

compensation magnet material (see Figure 1). Consequently, a weight penalty had

been incurred from these sources of flux leakage.

To circumvent the flux leakage problem, we have reconsidered the MSC circuit

f as an enclosed magnetic circuit. In this scheme, flux leakage is inhibited by

arranging ccmpensa*_or magnet pairs between the main wedge magnets and an outer

magnet sleeve (general-purpose steel) as shown in Figure 2. The triangular-shaped

compensator magnets, having alternating radial magnetization orientation as indicated

by the arrows, are ideally suited for developing the radial magnetomotive forces

which match perfectly the magnetic potential variation with azimuthal angle associated

with the wedge magnets. For the ideal. system having true radially and azimuthally

magnetized magnet components, no flux passes into the outer ferrous sleeve because

the compensation magnets are designed to operate at the normal coercivity point

(B - 0, H - H c ). However, given the monodirectionality of the rare-earth cobalt

magnet materials, some field distortions can be expected in fabricate3 structures.

These departures from the ideal field production patterns are expected to be most

severe with designs having few (4 or less) wedge magnets.

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Figure 2. Magnetic Sector CirctJt with New Boundary Matching Structure.

63% Transparency Factor Design.

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Weight saving is derived from two sources. First, the compensator magnets

are substantially smaller than the earlier design and second, the magnetic outer

shell serves a dual role as a mechanical support structure as well as a mechanical

housing for the compensator magnets.

Another feature to recommend the new conceptual approach to the MSC structure,

in addition to the more compact design, is the ability to provide a selectable

combination of peak magnetic field and ion-transmission, transparency factor. A

simple formulation of the " optimum" design parameters enables us to preselect the

magnetic focusing field level for differing ratios of the gap to magnet wedge

angles for a given set of mapetic materials (see next section).

2.0 MAGNET CIRCUIT DESIGN FORMUTATION

In this section, we indicate a method for choosing the compensator magnet

diue nsions for the " optimized" MSC design. The working model for this analysis is

shown schematically in Figure 3 for a polar sector containing one half period of

this rotationally symmetric structure. In the representation, the left-hand and

right-hand boundaries are at the same magnetic potential as the outer magnetic

sleeve, and the wedge magnet face ( part way along the vector rm in Figure 3) is

coincident with a maximum potential surface as drawn.

Assuming that the permanent magnet material is magnetized everywhere to the

same magnetization level, M, then we may derive a simple expression for the magnetic

field in the gap in terms of the fraction transparency parameters, fg:

fg - je g j/(je g j + le ml )

(1)

where eg is the angular separation between magnet faces in the vacuum-gap and e m is

the angular width of a wedge magnet. From the conservation of flux ( p • B - 0) and

from the vanishing curl of the field intensity ( 0 x H - 0) for a steady-state system

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Figure 3. Geometrical Layout of an MSC Sector.

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with negligible convection current, we may show that the magnetic flux density in +

the gap is uniform and has a value:

B - (1-fg ) 41TM (2)

To arrive at this expression, we have used the relation (emu):

B-H +4rM, (3)

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where, for an "ideal" permanent magnet, M is independent of the flux density, B,

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over the range of interest in the second quadrant of the hysteresis loop (assuming

'j SmCo material). The magnetization, 47M, is assumed to be equal t) the rermnent

flux density.

ti Now, we may obtain an expression for the radial thickness, h, of the

f compensator magnet with:

haro - rm , (4)

where rm is the radial location of the wedge magnet and r o is the extreme radial

location of the compensator magnet in the plane of the wedge magnet face (Figure

3). Using the same magnetostatic arguments as before, the following relationship

is derived (assuming Br - 0 everywhere):

h - rm 6m f g (1 - fg) (5)

A plot of the cofactor to the magnet azimuthal arc length is shown in Figure 4.

The maximum magnetic energy supplied to the gap occurs at a value of 0.5 for the

transparency factor. Magnetic efficiency remains high even to a transparency factor

value as high as 0.7 (70% transparency).

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3.0 MAGNETIC CIRCUIT ANALYSIS

To verify the validity of the formulation of the previous section, we have

performed simulations in polar coordinates, assuming that the structure has infinite

extent in the axial direction. Setting the magnization level at 0.9 T, we obtained

a gap field of nearly 0.45 T in the case of 50% transparency and 0.27 T in the case

of 67% transparency. Flux plots for these two cases are reproduced in Figures 5 and

6, respectively. (Staircased representation of the compensator magnet results from

the limitation of the simulation code for which boundaries must coincide with the

radial columns and azimuthal rows of the relaxed Liebmsnn net.) These plots correspond to a six-pole design with a four-inch outer diameter at an axial plane

where the diameter of the wedge magnet aperture is 0.8 inches.

While the simulation shows signs of incomplete relaxations after 5000

iterations, the flux density tabulations indicate clearly the basic e_`.fectiveness

of the compensator magnets in suppressing leakage flux in the radial direction.

Thus, the results of the computer calculations confirm the flux confinement properties

as well as the height determination, Equation 5.

4.0 WEIGHT SAVING

Weight reduction for the compensator magnet is approximately a factor of two

relative to the earlier MSC design at 50% transparency. No weight saving otherwise

is to be derived except with the more compact structural confinement afforded by

the outer "soft" magnet shell. How much weight saving is a matter of overall

system consideration, not proper to this design study.

5.0 RECOMMENDATIONS

The new conceptual methods for suppressing flux leakage is sufficiently

general, permitting a range of flux levels and transparency factors for the magnetic

sector circuit for use in a double-focusing mass spectrometer. Furthermore, the

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mechanical fabrication of the new configuration is not expected to complicate

assembly significantly ( aside from the fabricational cost which is expected to be

large,-). Thus, a lighter weight and more compact HSC structure appears workable.

Design of the detailed parts, assembly fixtures, and test fixtures should be

considere. 1 as the next step following decisions concerning the number of poles,

transparency factor and magnetic field level.

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