A device for measuring the distribution of masses in an atmosphere or plasma exploits the electrostatic deflection of ions in a rotating magnetic field. A magnetic field is not required. The device is simple to construct, can be made small, and is amenable to micromachining techniques such as LIGA (Lithographie-Abformung und Galvanoformung), or equivalent.

This so-called rotating-field (*rf*) analyzer transmits ions of a particular charge-to-mass ratio. One computes masses from this ratio by either knowing the charge from a separate measurement or making the usual assumption that each ion carries only one or a few units of charge. The device (see figure) consist of a rectangular parallepiped chamber with four conducting, insulated walls to which the *rf* voltages are applied, an entrance aperture, and a detector face. Dimensions are *x*_{0} × *y*_{0}× *z*_{0} with the Cartesian origin at the center of the ion-entrance aperture. Ions enter the device at a particular velocity v, polar angle *θ*, and azimuthal angle *φ*

[ where **v** = **x̂** sin*θ* cos*φ* + **ŷ** sin*θ* cos*θ + ***ẑ** cos*θ *],

Uniform, sinusoidally-oscillating orthogonal electric fields *E _{x }*and

*E*are established in the chamber by applying corresponding voltages

_{y}*V*and

_{x}*V*to the electrodes (omitted from the figure for clarity). The electric fields or applied voltages are made to oscillate at the same frequency

_{y}*f*, and 90° out of phase with each other, so that the resultant electric field rotates about the

**ẑ**direction with frequency

*f*. A straightforward analysis shows that, for homogeneous electric fields close to the axis, the

*x(T)*,

*y(T)*position of an ion between the plates is simply given by

*x(T) / λ _{x}* = cos

*ωt*− cos

_{0}*ω*(

*T + t*) −

_{0}*ω*sin

*ωt*(1a)

_{0}y(T) / *λ _{x}* = sin

*ωt*sin

_{0}−*ω*(

*T + t*)

_{0}*− ω cos ωt*(1b)

_{0}Here, *ω*= 2*π**f *is the angular frequency, *T *is the time the ion spends in the dipole fields, and *t*_{0} is the time of arrival of the ion at the entrance aperture relative to the phase of the *rf *field. The assumption of zero velocity perpendicular to the axis has been made for simplicity. The quantities

are scaling parameters, which describe the amplitude of ion motion between the plates. This amplitude is seen to be linearly proportional to the charge-to-mass (*e/m*), electric fields (*V _{x}*/

*x*

_{0},

*V*/

_{y}*y*

_{0}), and inversely proportional to

*ω*². To see how the output pattern at the detector plane

*z*=

*z*looks, one would first define the incident particle velocity, then "tune" the

_{0 }*rf*angular frequency so that

*ωT*=

*2π*for that velocity. In this case, one can obtain the simple expression

*x ^{2}(T) / λ_{x}^{2} + y^{2}(T) / λ_{y}^{2} *= 1

Hence, the locus of points at *z* = *z _{0}* is a circle for each

*e/m*. This is similar to the familiar Lissajous figures one makes with electrons and an oscilloscope. The figure could be detected by an area detector, such as a microchannel plate or a charge-coupled device. The resolution of the device, or separation between adjacent

*e/m*, will depend on the input- aperture diameter, angular width of the incident beam, and homogeneity of the fields. Some of these effects can be obtained by taking suitable differentials of Eqs. 1a and 1b.

To confirm the behavior in Eqs. 1a and 1b, computer simulations of this device were carried out using a three-dimensional, non-space-charge limited fields-and-trajectories code. The device was also tested in the laboratory using a cell of dimensions 2 mm × 2 mm × 20 mm. Mass spectra were obtained from a commercial ion source. Since the input energies of the ions from the source were equal, but the input velocities could not be made equal, each ion was detected by "tuning"*ω *to its particular velocity, then detecting its transmitted current. One could also use the device as a velocity selector by detecting only those ions with a specific z-component of velocity given by *v* cos *θ *= *z*_{0}/*T*. For this, one would pulse the ions into the cell, then gate the detector "on," after the interval *T*. Suggestions along these lines were reported earlier in, "Ballistic Mass and Velocity Analyzer"*NASA Tech Briefs* (NPO-19235), Vol. 20, No. 6, (June 1996) page 57.

*This work was done by Steven J. Smith and Ara Chutjian of Caltech for *NASA's Jet Propulsion Laboratory.* For further information access the Technical Support Package (TSP) **free on-line at www.techbriefs.com **under the Physical Sciences category, *or circle no. 153 *on the TSP Order Card in this issue to receive a copy by mail ($5 charge).*

*In accordance with Public Law 96-517, the contractor has elected to retain title to this invention. Inquiries concerning rights for its commercial use should be addressed to*

###### Technology Reporting OfficeJPLMail Stop 122-1164800 Oak Grove DrivePasadena, CA 91109(818) 354-2240

*Refer to NPO-19682, volume and number of this *NASA Tech Briefs* issue, and the page number.*

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This article first appeared in the February, 1998 issue of *NASA Tech Briefs* Magazine.

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