optical diagnostics options for bismuth hall thrusters · optical diagnostics options for bismuth...

American Institute of Aeronautics and Astronautics

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Optical Diagnostics Options for Bismuth Hall Thrusters

David B. Scharfe* and Mark A. Cappelli†

Stanford University, Stanford, CA, 94305

A bismuth-fed Hall thruster has recently been selected for further development as a potential solution for faster missions to the outer planets. With higher efficiency and higher power handling, this two-stage Thruster with Anode Layer (TAL) should meet the necessary requirements for such missions. As the thruster is developed, there will be a need for non-intrusive diagnostic methods to optimize the geometry and operating conditions. Such optical diagnostic methods for analyzing the velocity, energy, and number densities of BiI and BiII are developed and discussed here. Candidate transitions are selected and their lineshapes modeled with respect to hyperfine splitting and broadening mechanisms. Suitable transitions are selected on the basis of relative strength, hyperfine data, and accessibility to tunable diode lasers; candidate transitions include the 306.86, 784.25, and 854.7nm lines of BiI and the 143.68, 796.7, and 854.3nm lines of BiII. Preliminary spectrum measurements using a microwave discharge are presented and future work is discussed.

Nomenclature A = magnetic moment hyperfine splitting parameter a = Voigt “a” parameter B = quadrupole moment hyperfine splitting parameter ∆E = energy shift due to hyperfine splitting by nuclear spin ∆λ = shift in wavelength/frequency from linecenter ∆v = integrated range of wavelengths/frequencies ∆vx = lineshape FWHM due to broadening mechanism, xE = energy between two electronic states F = total atomic angular momentum quantum number, including nuclear spin f12 = oscillator strength φx = lineshape function for broadening mechanism, xI = nuclear spin quantum number Iv/I0,v = ratio of transmitted to incident light intensity at a given wavelength/frequency, vIn = relative intensity of hyperfine split transition J = total atomic angular momentum quantum number, excluding nuclear spin j = single electron angular momentum quantum number kv = spectral absorption coefficient L = total orbital angular momentum quantum number La = absorption path length λ,v = wavelength or frequency of light m = atomic mass n = number density S = total electron spin angular momentum quantum number S12 = linestrength T = kinetic temperature u = bulk velocity v0 = linecenter frequency w = parameter indicating distance from linecenter

* Research Assistant, Mechanical Engineering Department, Building 520. Member, AIAA. † Associate Professor, Mechanical Engineering Department, Building 520. Member, AIAA.

40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit11 - 14 July 2004, Fort Lauderdale, Florida

AIAA 2004-3946

Copyright © 2004 by Stanford University. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


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I. Introduction S the goals of space flight reach toward faster missions to the outer planets, issues of spacecraft mass, efficiency, and flight time become increasingly important. The increase in velocity-increment required to

significantly reduce the time of flight requires that either the propellant mass or the specific impulse (Isp) of the thruster be increased. Electric propulsion systems, like those flown on Deep Space I, have shown significant benefits over conventional chemical propulsion methods. However, state-of-the-art systems are still lacking in the efficiency and power handling required for the development of feasible Nuclear-Electric Propulsion (NEP) missions to the outer planets. Present ion engine technology is limited in power to less than 10kW, while such future missions would require several times that amount.

In order to accommodate the requirements of mid- and far-term NEP missions, NASA recently selected a bismuth-fueled two-stage Hall Thruster with Anode Layer (TAL) for further development‡. This Very High Isp TAL (VHITAL) builds on the TAL 160 and TAL 200 thrusters developed to operate on storable metal vapor propellants by TsNIIMASH in Russia. A bismuth-fed Hall thruster offers significant advantages over ion thrusters; current TAL thrusters have been demonstrated to perform at 25-140kW and have the potential to scale up to greater than 500kW for future very high power NEP systems. Additionally, the bismuth propellant offers several advantages over the xenon propellant used in current ion thrusters. Bismuth has a larger atomic mass, which serves to increase thrust for a given particle flux. Additionally, it is condensable at room temperature, which allows for simpler testing on the ground in existing facilities as well as reduced spacecraft tankage fraction. Bismuth is also significantly less expensive and more readily available than is xenon, and has a lower ionization potential yielding higher efficiency.

As the Bi-fed Hall thruster is developed, precise optimization of geometry and operating conditions, as well as accurate predictions of the potential for spacecraft contamination, will be contingent upon a characterization of the internal and near-field neutral bismuth (BiI) and bismuth ion (BiII) energy distribution, velocity field, and particle flux. A combination of laser-induced fluorescence (LIF) and absorption spectroscopy will be used to perform a portion of the necessary diagnostics.

This paper will discuss the optical diagnostics options for bismuth, and the development of the necessary spectroscopic methods for measurement of particle characteristics in the near-field of a bismuth Hall thruster. It is expected that LIF will be used to probe excited states in the BiI and BiII atomic and ionic particle stream to deduce the three-dimensional (3D) velocity (energy) distribution. While several electronic transitions of neutral and ionized bismuth are accessible with laboratory-laser systems (e.g., Ti-Sapphire or Ring-Dye lasers), they are not easily accessed with more compact laser sources that are more conveniently used in ground-test facilities suitable for thruster performance studies. In this respect, we will discuss alternative spectroscopic options that are more accessible with compact tunable, narrow-band diode lasers. We will develop models for spectral absorption/fluorescence lineshapes of transitions of interest – models that are necessary for correct interpretation of the measurements of particle velocities within the thruster.

In addition to measurements of particle velocity, we will review the possible options for measuring BiI and BiII ground state densities and/or electron number density. These density measurements, along with measurements of velocity, will be used to determine particle flux to critical engine components and used as boundary conditions for calculations of the propagating plume for spacecraft contamination predictions. One possible option for ground state BiI number density will be the use of atomic resonance absorption spectroscopy of the 306.86nm (6p3 4S3/2 – 7s 4P1/2) transition using a Bi hollow-cathode lamp as a narrow line source. For BiII, a transition with the ground state as the lower state is located at 143.68nm (6p2 3P0 – 7s 3P1). Estimates of absorption measurements for BiI and BiII will be discussed.

Preliminary experimental measurements of probing near infrared transitions of bismuth in a microwave discharge will be presented to illustrate the necessity of certain design considerations for these purposes.

II. Transitions and Lineshapes For the purposes of this study, relatively strong lines (transitions) in the near IR (roughly 700-900nm) are

desirable for velocity measurements for their accessibility via laboratory laser systems. While a wide range of lines can be accessed via more complex laser systems, the subset of lines accessible to off-the-shelf tunable diode lasers are preferred for these LIF measurements. For example, the New Focus TLB-6000 Vortex series lasers can be configured for scanning small wavelength ranges located approximately within 765-788nm and 795-853nm§. For

‡ See, for example: http://www.aviation now.com/content/ncof/ncf_n84.htm and press release: http://quest.arc.nasa.gov/aero/news/08-30-02.txt. § See http://www.newfocus.com/product/modelgroup.cfm?productlineid=1&modelgroupid=1121&app=photonics

A


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purposes of number density determination, a line that is coupled to the ground state is desired for use in atomic resonance spectroscopy. In order to make accurate density and velocity measurements, an understanding of the lineshapes of these transitions is required.

A. Electronic Transitions The ground electronic state of neutral bismuth is given by:

[ ] 3/24321014 S6654 psdfXe ,

and that of singly ionized bismuth is:

[ ] 03221014 6654 PpsdfXe .

Each electronic state of any species can be denoted by a term symbol given by 2S+1LJ. In this notation, S is the total electronic spin angular momentum, 2S+1 is the multiplicity of the state, L is the total orbital angular momentum, and J is the total angular momentum of the atom. For example, for the ground state of neutral bismuth, the spin is 1/2, Lis 0, and J is 3/2; for the ground state of the bismuth ion, S is 1, L is 1, and J is 0.

A listing of the term symbols, configurations, and energy levels of the various electronic states of neutral and ionized bismuth can be found in the literature1-3. Diagrams of these electronic states are given in Figs. 1 & 2, where the notation near each line indicates the configuration of the outermost or excited electrons. States of BiII denoted with a prime indicate the excitation of j, the angular momentum of an individual electron, from 1/2 to 3/2 in the next outermost electron. Although so-called forbidden transitions can occur (especially for atoms with many electrons), in general transitions between electronic states of a given species can be defined by the selection rules:

.1,01

0

±=∆±=∆

=∆

JLS

Figure 1. Overview of the energy level system of Bi I. Figure 2. Overview of the energy level system of Bi II.


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The energy difference between the states of an allowed transition defines the wavelength of emitted (or absorbed) light according to:

.Ehc=λ (1)

Here, λ is the wavelength of light, h is Planck’s constant, c is the speed of light, and E is the energy difference between two states (the energy of the emitted photon).

B. Hyperfine Splitting The above would imply that only a single discrete wavelength would characterize each electronic transition;

however, the role of multiple isotopes and the nuclear spin, I, split each electronic state into multiple closely spaced energy levels. The effect is what is termed hyperfine splitting and results in each electronic transition being divided into multiple closely spaced discrete wavelengths (energies) of varying intensity.

For the case of bismuth, only one stable isotope naturally exists, so isotopic splitting will not be discussed here. To determine the splitting of each electronic state due to nuclear spin, we first note that the value of the nuclear

spin, I, for bismuth is 9/22. For a single isotope of any species, the splitting of an electronic state is defined by energy shifts, ∆E:

( ) ( ) ( )( ) ( ) ,

1212811413

21

−−++−++=∆

JJIIJJIICCBACE (2)

where:

( ) ( ) ( ).111 +−+−+= JJIIFFC (3)

In the above equations, F is the angular momentum including nuclear spin and can take on multiple values according to:

,...,,1, IJIJIJF −−++= (4) where J is the total angular momentum for the electronic state considered. It should be noted, however, that for a high nuclear spin like that of bismuth, J is typically smaller than I so that the total number of F values is limited to 2J + 1. A and B are hyperfine splitting parameters for a given electronic state and relate to the magnetic moment and the interaction of the quadrupole moment with the electron shell, respectively. Many of the electronic states of BiI and BiII have been studied to determine A and B and the values calculated from various experiments are tabulated in Refs. 2 and 3. Selections of these values for the states (transitions) of interest in this study are compiled in Tables 1 and 2; uncertainties and the results of previous works are presented in the references. To predict the splitting of an electronic transition, an additional selection rule is considered for transitions between the F-states of upper and lower electronic states:

,1,0 ±=∆F

Table 1. Values of the Magnetic-Dipole A and Electric Quadrupole B coupling constants for select BiI states3.(1mK = 10-3cm-1)

Level E (cm-1) A (mK) B (mK) 6p3 4S3/2 0 -14.76 -10.8 7s 4P1/2 32588.21 164.171 -- 6p3 2P3/2 33164.805 16.27 34.20 7s 4P3/2 44865.076 -2.02 -21.58 7s 2P1/2 45915.883 -143.72 --

Table 2. Values of the Magnetic-Dipole A and Electric Quadrupole B coupling constants for select BiII states2.(1mK = 10-3cm-1)

Level E (cm-1) A (mK) B (mK) 6p2 3P0 0 -- -- 7s 3P1 69598.475 390.7 3 7p 3D2 88789.478 123.35 -12 6d 3P1 100494.931 108.4 11 8s 3P1 101340.430 279.8 6


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but with F = 0 to F = 0 forbidden. Calculations using the above equations and selection rules for transitions between the split states of an upper and lower electronic state will give the discrete wavelengths of the corresponding hyperfine split transition. The relative intensities, In, of the lines for a given hyperfine split transition are calculated from the sum rules4, which translate to the formulas5:

For J → J transitions:

( )( )( )( )F

IFJIFJIFJIFJIn FF

−−++−−++++−=→−

111

( ) ( ) ( )[ ] ( )( )1

12111 2

+++−+++=→ FF

FIIFFJJIn FF

( )( )( )( )1

1121 +

−−−+−+−++++−=→+ F

IFJIFJIFJIFJIn FF (5)

For J-1 → J and J → J-1 transitions:

( )( )( )( )F

IFJIFJIFJIFJIn FF

111

−−+−++++++−=→−

( )( )( )( )( )( )1

1211+

+−−−+−−++++−=→ FF

FIFJIFJIFJIFJIn FF

( )( )( )( )1

2111 +

−−−−−−−+−+−=→+ F

IFJIFJIFJIFJIn FF (6)

Using the above, a discrete line spectrum can be produced to predict the hyperfine splitting of a given transition, provided that the upper and lower states are known and that the hyperfine constants A and B can be found for each. For example, the calculated hyperfine structure for the 306.86nm (6p3 4S3/2 – 7s 4P1/2) transition of BiI is shown in Fig. 3. In this transition, the splitting constants are A =-14.76mK, B = -10.8mK for the lower (ground) state and A= 164.171mK for the upper state3 (note that 1mK=10-3cm-1). It should be noted here that because J = 1/2 for the upper state, B must be taken as zero to avoid numerical problems with Eq. (2). The hyperfine structures of other transitions are shown in later figures along with associated lineshape profiles, discussed below. In all plots, intensities are normalized so that the maximum hyperfine-split line has amplitude 100.

C. Lineshape Broadening When taking measurements on a Hall thruster like the

VHITAL system, the hyperfine peaks are expected to be broadened to form a more continuous lineshape. An analysis of the causes of this broadening is necessary for thruster diagnostics.

Assuming that an electronic transition is probed using a tunable laser (such that instrument broadening can be neglected), broadening mechanisms can be grouped into

Figure 3. Hyperfine structure of 306.86nm (6p3 4S3/2 –7s 4P1/2) transition in BiI. ∆λ represents the frequency shift relative to linecenter, 32588cm-1.


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two main categories: those that result in a Lorentzian lineshape and those that result in a Gaussian lineshape. Lorentzian broadening mechanisms include lifetime, natural, collisional, Stark, and resonance broadening. An example of a Gaussian broadening mechanism is Doppler broadening, which is the result of a thermal velocity distribution of particles; this is in addition to the Doppler-shift of a spectral feature due to the average or bulk velocity of particles.

Of primary interest for thruster diagnostics is the Doppler shift of a transition, which indicates the average exhaust velocity of neutrals or ions. The mean velocity, u, corresponding to a given shift in transition frequency, δv,is given by:

,0vvcu δ= (7)

where v0 is the unshifted linecenter frequency and c is the speed of light. Doppler broadening, indicating the Maxwellian spread in particle velocities, can be used to determine the velocity distribution function of neutrals. The ion velocity distribution in a Hall thruster plume is related to the spatial distribution of the ionization zone relative to thruster potential and does not necessarily produce a Maxwellian distribution6, so quantitative lineshape models may not strictly apply to BiII, but will still be presented here as an understanding of the lineshape is still necessary for correct determination of Doppler shifts.

The lineshape function, φ, for a Doppler broadened transition (single peak) as a function of frequency, is given by:

,2ln4exp2ln2)( 0

2/1

∆−

−

∆=

DDD v

vvv

vπ

φ (8)

where v0 is again the linecenter frequency. ∆vD is the Doppler FWHM, given by:

,2ln8 2/1

20

=∆

mckTvvD (9)

where k is Boltzmann’s constant, T is the kinetic temperature, m is atomic mass, and c is again the speed of light. In Eq. (8), the term before the exponential is a normalization constant so that the lineshape integrated over all frequencies is equal to unity; this factor need not be considered in examining a recorded lineshape. Provided that the Doppler broadening effects are much larger than the Lorentzian mechanisms, the above would be applied to the multiple hyperfine peaks of an electronic transition and used to determining the velocity distribution function from a lineshape. However, due to the presence of other broadening mechanisms, the Doppler lineshape is typically convolved with a Lorentzian lineshape to produce a Voigt profile. A purely Lorentzian lineshape is given by:

( ),

221)( 2

20

∆+−

∆=

L

LL

vvv

vvπ

φ (10)

where ∆vL is the FWHM corresponding to the particular Lorentzian broadening mechanisms present. For example, for the case of resonance broadening, the FWHM is given by:

( ) ,2

8

0

122

2' nm

fec

ckve

resjjres ε

λππ=∆ (11)

where kjj’ is a constant relating to the quantum numbers of the ground and resonance levels, c is the speed of light, eis the electron charge, and f12 and λres are the oscillator strength and wavelength of the transition, respectively. ε0 is the permittivity of free space, me is the electron mass, and n is the number density of the perturbing state. When a Lorentzian is convolved with a Doppler or other Gaussian profile, the lineshape becomes:


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,)()()( ∫∞

∞−−= duuvuv LDv φφφ (12)

which can be manipulated into:

( )( ).),()(

exp)()(

0

22

2

0

waVv

dyywa

yavv

D

DV

φπ

φφ

=−+

−= ∫∞

∞− (13)

This is the equation for a Voigt profile. The Voigt “a” parameter indicates the ratio of Doppler to Lorentzian broadening and is given by:

,2ln

D

L

vva

∆∆= (14)

while w is a parameter indicating the distance from linecenter, and is given by:

( ).

2ln2 0

Dvvvw

∆−

= (15)

D. Modeled Lineshapes For purposes of number density determination of BiI, the line at 306.86nm, which is coupled to the ground state,

will likely be used in atomic resonance absorption spectroscopy, which can incorporate a measurement of the Lorentzian broadening if experimental resolution is high enough to detect the lineshape. For number density

Figure 4. Doppler Broadening of 796.7nm (7p 3D2 – 8s 3P1) transition in BiII. :, T=11500K; --, T=115000K; ―, T=500000K; |, hyperfine transitions. ∆λ represents the frequency shift relative to linecenter, 12552cm-1.

Figure 5. Doppler Broadening of 854.3nm (7p 3D2 – 6d 3P1) transition in BiII. :, T=11500K; --, T=115000K; ―, T=500000K; |, hyperfine transitions. ∆λ represents the frequency shift relative to linecenter, 11705cm-1.


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estimates of BiII, the ground state can be excited via a transition at 143.68nm (6p2 3P0 – 7s 3P1); note that this line is a forbidden transition since ∆L = 0, but it has been recorded successfully with relatively high intensity2. For the neutral line, a Bi hollow-cathode lamp can be used as a broadband lightsource; other options would need to be developed for the ion line. In the near IR region, the candidate transitions of interest for velocity measurements of BiI are at 784.25nm (6p3 2P3/2 – 7s 2P1/2) and 854.7nm (6p3 2P3/2 – 7s 4P3/2)1,3,8; both of these lines are forbidden due to ∆L = 0, but have been recorded and analyzed successfully3. Candidate transitions for velocity measurements of BiII are at 796.7nm (7p 3D2 – 8s 3P1) and 854.3nm (7p 3D2 – 6d 3P1)1,2,8. These near IR lines are relatively strong2,3,8,reachable with off-the-shelf tunable diode lasers, and have available hyperfine splitting constants in the literature2,3.

Lineshapes that are purely Doppler broadened can be calculated directly from Eq. (8). The broadening of each hyperfine-split peak can be calculated and profiles can be summed where they overlap. Though it is unlikely that the ions exiting the thruster will obey a thermal velocity distribution, we can nonetheless model such profiles as in Figs. 4 and 5 for the BiII transitions given above. In the plots presented here, the peak of each Doppler broadened profile (i.e. φD(v0)) has been equated to the normalized amplitude of its corresponding hyperfine peak; where the broadened profile reaches above the hyperfine line spectrum indicates that the profiles of two peaks have overlapped and were summed. Note that T in these plots is the kinetic temperature and corresponds to the Doppler FWHM of the broadened profiles. In theory, the broadening of these transitions due to the velocity distribution function will provide an idea of the size and shape of the ionization zone relative to the thruster potential.

Determining the Voigt profile of each transition is less direct a calculation. The Voigt function, V(a,w), in Eq. (13) can be calculated from standard mathematical routines or by making use of existing tables; in this work we have used a Matlab code with an algorithm developed by Humlíček7 to approximate Voigt lineshapes of the hyperfine split transitions; overlapping profiles are summed as with the Doppler lineshapes. The results of this model for BiII transitions of interest are shown in Figs. 6 and 7, shown here for temperatures corresponding to a ~10eV (kinetic temperature 115,000K) spread in velocities. A plot for the 143.68nm transition of BiII is not included as the hyperfine splitting constants could not be found for the ground state of BiII. In Fig. 8, the Voigt broadened profile for the resonance transition in BiI is shown for several a values and a Doppler broadening corresponding to 500K. The same is repeated for the candidate near-IR lines of BiI in Figs. 9 and 10. This low temperature for BiI is on the order of room temperature and corresponds to approximate observations for neutrals in other laboratory Hall thrusters6; this estimate may be affected somewhat by the need to preheat a bismuth propellant.

Figure 6. Voigt Broadening of 796.7nm (7p 3D2 – 8s 3P1) transition in BiII. T=115000K; ―, a=0; :, a=0.5; --, a=2; |, hyperfine transitions. ∆λ represents the frequency shift relative to linecenter, 12552cm-1.

Figure 7. Voigt Broadening of 854.3nm (7p 3D2 – 6d 3P1)transition in BiII. T=115000K; ―, a=0; :, a=0.5; --, a=2; |, hyperfine transitions. ∆λ represents the frequency shift relative to linecenter, 11705cm-1.


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Figure 8. Voigt Broadening of 306.86nm (6p3 4S3/2 – 7s 4P1/2) transition in BiI. T=500K; ―, a=0; :, a=0.5; --, a=2; |, hyperfine transitions. ∆λ represents the frequency shift relative to linecenter, 32588cm-1.

Figure 9. Voigt Broadening of 784.25nm (6p3 2P3/2 – 7s 2P1/2) transition in BiI. T=500K; ―, a=0; :, a=0.5; --, a=2; |, hyperfine transitions. ∆λ represents the frequency shift relative to linecenter, 12751cm-1.

Figure 10. Voigt Broadening of 854.7nm (6p3 2P3/2 – 7s 4P3/2) transition in BiI. T=500K; ―, a=0; :, a=0.5; --, a=2; |, hyperfine transitions. ∆λ represents the frequency shift relative to linecenter, 11700cm-1.


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E. Number Density Determination In order to calculate the number density corresponding to a measured transition (i.e.: absorption of the 306.86nm

transition in BiI, or the 143.68nm transition in BiII), a form of Beer’s Law is used:

( ) ( ) ,)(exp)(expexp 121

2

12,0

−=−=−= a

eaav

v

v Lvfncm

eLvSLkII

φπφ (16)

where I0,v and Iv are the incident and transmitted intensities at a given wavelength, respectively, with units of power per unit area per unit spectral frequency. kv is the spectral absorption coefficient, La is the path length through the absorbing medium, S12 is the linestrength, φ is the previously-discussed lineshape function, f12 is the oscillator strength of the measured transition, and n1 is the number density of the absorbing (ground) state. e is the electron charge, me is the mass of an electron, and c is the speed of light. We would like to predict the sensitivity of this method for determining the necessary densities in the thruster. For the absorption measurement of the BiI resonance transition, a bismuth hollow cathode lamp will likely be used as a broadband light source near 307nm. If the experimental apparatus had infinitely fine resolution, the precise absorption lineshape could be measured and Eq. (16) could be used to quantitatively determine the number density. However, any instrument used to collect the transmitted light would have a finite range of collected wavelengths, producing an artificially broadened profile. Because of this, only relative number densities can be calculated, based on the relative areas of different absorption profiles. To predict the absorption under these circumstances, typical values for the type of thruster being developed were used9; with an ion current of 70mA/cm2, an exhaust velocity of 70km/s, and a propellant utilization on the order of 90%, it can be shown that the ion number density is roughly 6x1010cm-3 and the neutral density is on the order of 5x1012cm-3. The oscillator strength is 0.146 for the BiI resonance line8 and the thruster diameter is expected to be less than 40cm9. Based on this data, Eq. (16), and appropriate data-point averaging to simulate instrument resolution, the plots of Fig. 11 were produced to illustrate practical absorption measurements for different path lengths and resolutions. Note that the smallest absorption fraction is still on the order of a few percent and should be resolvable. For the case of ionized bismuth, similar measurements would become significantly more problematic. The number density of the ions is two orders of magnitude smaller than that of BiI, resulting in absorption that is likely to be lost in system noise. Additionally, the BiII measurement would correspond to a wavelength of 143.69nm, in the vacuum ultraviolet where few measurement techniques are available. Finally, the hyperfine data of this transition is currently lacking, hampering the development of lineshape models.

Figure 11. Absorption profiles for 306.86nm transition of BiI with 500K Doppler broadening. From left to right: trueabsorption profile, profile corresponding to 1 Angstrom instrument resolution, and profile corresponding to 0.2 Angstrom resolution. All plots have different axis scales. In all plots: ―, absorption length = 1cm; --, length = 20cm; :, length = 60cm. λ is wavelength.


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III. Preliminary Measurements A microwave discharge tube was purchased and used in an attempt to record the bismuth transitions and their

relative strengths as they may show up in a bismuth-fueled Hall thruster. This selection was made as a microwave discharge can typically produce measurable ion densities, while other options (ie: hollow cathode lamps) typically only produce measurable neutral features. The tube was constructed using neon as a carrier gas, and bismuth iodide as the source for atomic bismuth. The presence of the iodine was intended mainly to react with bismuth as it plated out onto the tube walls so that optical integrity would be preserved. The tube was used in an Evenson Cavity with a microwave power supply, and observed using both a half-meter scanning monochromator with PMT and an Ocean Optics spectrometer.

Initial measurements show that, while neon and iodine lines show up clearly in recorded spectrums, the bismuth lines are for the most part significantly weaker and could not be confidently identified. An additional difficulty in identifying bismuth features with the chosen apparatus was that several iodine lines lie very close in frequency to Bismuth lines so that the two could not be resolved from each other. One of the preliminary spectrums is presented in Fig. 12. Note that at 699nm appears a peak that may match a bismuth line, but is more likely a measurement of the iodine transition at essentially the same wavelength. Other such ambiguous and difficult to resolve transitions have been recorded with this tube where bismuth has spectral features very close to those of iodine and neon. Because of these issues, a different design or a completely different apparatus (i.e., a bismuth arc lamp) may be more functional for preliminary measurements.

IV. Conclusion We have provided here all necessary equations for modeling the lineshape of any bismuth transition; these

lineshapes are required for accurate interpretation of data for velocity and number density measurements. Candidate transitions for both BiI and BiII were selected and modeled for various broadening conditions. For measurements of velocity, it should be a trivial exercise to alter the temperature or Lorentzian broadening conditions to closely match a recorded lineshape. Ideally, the models used here will be incorporated into a curve-fit optimization algorithm so that T and a can be varied simultaneously to determine which parameters best fit recorded data. It is noted here that in the case that the candidate transitions are too weak to record in a Hall discharge, other transitions can be selected and modeled using the same set of equations with little difficulty, provided that the splitting parameters are available. Alternatively, if the restriction of using transitions for which the hyperfine constants are known limits us to transitions that cannot be detected in a Hall thruster, there is the option for choosing stronger transitions and using

700 720 740 760 780 800 820 840 860 880 900λ (nm)

BiIBiIINeINeIII I and I IIMeasured Spectrum

Figure 12. Preliminary recorded spectrum of bismuth microwave discharge. λ is wavelength.


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other techniques to first determine the hyperfine structure. The restriction of accessibility to diode lasers, too, will simplify future measurements but is not an absolute necessity.

For measurements of BiI, current techniques and practical instrument resolutions will limit analysis to only qualitative or relative measurements of the number density. For a similar absorption measurement probing the ground state of BiII, difficulties yet to be explored include very weak absorption due to low number density, obtaining an appropriate apparatus and technique for operation in the vacuum ultra violet, and overcoming the lack of hyperfine data on the BiII ground state. Other methods will be explored for future analysis.

Acknowledgments This research was supported in part by the Air Force Office of Scientific Research and by the National

Aeronautics and Space Administration. Stipend support for D. Scharfe was provided through a fellowship from the Department of Defense/ASEE.

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Standards, Circular 467, U.S. Government Printing Office, Washington, D.C., 1958, May 1, 1958, pp219-222. 2Dolk, L., Litzen, U., and Wahlgren, G.M., “The Laboratory Analysis of Bi II and its Application to the Bi-rich HgMn Star

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Aerospace Sciences Meeting & Exhibit, AIAA, 14-17 January 2002.

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