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IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 32, NO. 4, AUGUST 2004

TABLE II

COMPARISON BETWEEN FIELD MAGNITUDES PREDICTED BY THE XFDTD MODEL AND

THOSE CALCULATED FROM FORWARD (F) AND REFLECTED (R) POWERS AT 1 GHz

and BSS saturated glass fiber filter), measurements were per-

not presently available in our laboratory. A comparison of the

field and

at their respective maxima

formed using an open-ended dielectric probe kit13 in conjunction

magnitudes of the

in the standing wave pattern in the waveguide at a frequency

with an automated vector network analyzer (HP model 8720B).

of 1 GHz showed good agreement for forward powers in the

In making these measurements and applying the results to the

range 0.5­5 W (Table II). The fact that the computations based

XFDTD model, a number of issues needed to be addressed to

on waveguide theory utilized values of power measured by

achieve accurate reliable results [17].

a wattmeter having a manufacturer-specified accuracy of 5%

One issue was the minimum thickness of material required

could have contributed to differences between the two methods

to obtain accurate dielectric property measurements. In the case

(maximum difference 8.5%). Moreover, XFDTD simulations

of materials with high water content, the open-ended coaxial

took into account field disturbances from the probe launch and

probe technique provides accurate dielectric properties with a

waveguide slots, whereas computations based on waveguide

minimum sample thickness of 5­6 mm in the frequency range

theory did not.

of interest [18], [19]. Other dielectrics typically require a greater

Surface plots of the  field and  computed at a frequency

thickness that depends on the value of the dielectric constant of

of 1 GHz and a forward power of 0.5 W are presented in Fig. 6.

the material. For the BSS-saturated glass fiber filters it was es-

plane of the waveguide

The results are plotted in the central

tablished that a sample thickness equivalent to that of 20 stacked

at the location where the glass fiber filter would be placed in

filters, i.e., an approximate thickness of 5.2 mm was sufficient

experiments. Here the  axis is along the longer cross-sectional

to give accurately measured dielectric data. In the case of the

dimension, the axis is along the shorter cross-sectional dimen-

dental putty and Plexiglas, a thickness of 16 mm was sufficient.

sion, and the axis is along the length of the waveguide (Fig. 4).

The permittivity of BSS and a BSS saturated glass fiber filter

It is observed that the distances from the shorting plate of the two

changed with frequency as expected for a first-order Drude ma-

existing  field maxima are 16.31 and 35.20 cm, respectively.

terial [11]. The Plexiglas and dental putty permittivities did not

This provides an estimated waveguide wavelength of 37.8 cm,

change appreciably within the frequency range of interest.

which is the same as the theoretical value. The  maximum oc-

The second issue was whether the presence of the chromaffin

curred at a quarter waveguide wavelength from the  maximum

cells on the glass fiber filter appreciably affected the dielectric

as expected from theory. In addition, the magnitudes of  and

properties of the filter. To determine this, dielectric property

at the maxima were computed by XFDTD to be 172.3 V/m

measurements were made on a suspension of 8 million chro-

and 4.49 T, respectively. These values agree well with the values

maffin cells in 20 ml of BSS, the maximum number of cells

172.2 V/m and 4.57 T predicted by waveguide theory.

that are used in experiments. A difference of less than 2% was

The overall field patterns computed by XFDTD [Fig. 6(b)]

measured in the dielectric properties of BSS with cells and BSS

and predicted by waveguide theory based on measurements of

alone, which is in agreement with published results [20], [21].

forward and reflected power [Fig. 6(a)] agree closely. Although

This suggests that the presence of the cells can be ignored when

the XFDTD model takes into account the near field of the probe

modeling the glass fiber filter.

launch, which rapidly falls off with distance from the probe, this

does not appear to affect the overall standing wave pattern in

III. RESULTS AND DISCUSSION

the waveguide. Also, even though the overall  patterns were

A. Model Validation

in agreement, the XFDTD plots revealed small features not pre-

To test the accuracy of the XFDTD model, the numerically

dicted by theory. For example, small ripples in the second max-

computed  field and  within the waveguide, in the absence

imum of the  component of  were localized in a region of

of the cell perfusion apparatus, were compared with those

the subgrid in the vicinity of the top and bottom slots in the

computed from well-known waveguide theory [22] based

waveguide walls. These features disappeared when the top and

on measured values of forward and reflected power. Actual

bottom slots were not implemented in the model. Also, in the

fields and

in the waveguide were not

measurements of

region of the same standing wave maximum, there were small

performed because nonperturbing field measuring probes are

local maxima and minima in the  component of  along the

subgrid boundaries in the  direction. These variations existed

over a width of a single Yee cell (0.3048 cm) along the  axis

and ceased to exist outside the subgrid. The variations remained

13Hewlett

Packard (HP) model 85 070A, Palo Alto, CA