Investigation of Instabilities and Scaling Effects on

steady-state AF-MPDT SX3

MSc student Luca Malacci - University of Pisa Supervisors.: Prof. Georg Herdrich, Prof. M. Andrenucci, PhD Candidate Adam Boxberger

•  Investigate possible critical regimes in the SX3 •  Analysis of different criteria in order to predict instabilities occurrence •  Comparison of operational regime with existing experimental data •  Experimental test with predetermined operational parameters* •  Assessment of the results

*All these tasks, especially experimental ones, have to be performed accordingly with the present available hardware at IRS, taking into account timing and feasibility of the procedure.

SF-MPDT: Self-field •  Propellant (Ar, Li, He, Xe, H) is injected

in an acceleration chamber consisting in two coaxial electrodes

•  Acceleration process is mainly due to the interaction between the self-field magnetic field and the current density j, according to the momentum eq.:

AF-MPDT: Applied-field •  Externally imposed magnetic field allows

to increase efficiency at low-mid power regime (up to 100 kW) [5]

•  4 acceleration processes [5]: –  Self-magnetic acceleration –  Swirl acceleration –  Hall component –  Gas-dynamic acceleration: Joule heating and expansion of the

gas in a physical or magnetic nozzle

€

ρdudt

= −∇p + j × B (1)€

j r × Bθ j z × Bθ

j r × Bz j z × Br

jθ × Bz jθ × Br

Acceleration process is derived by the generalized Ohm’s law, eq (2)

€

j = σ E + u × B][ −ωeτe

Bj × B[ ] (2)

Since Hall currents in azimuthal directions can only take place trough a particle colllisional process, the Hall parameter (according eq 3) is a characteristic variable for AF-MPDs operation:

The first two factors on the right-hand side are respectively the gyration frequency an mean free path period of electrons. Hall parameters has the meaning of a ratio of gyration frequency of electrons to the related collision frequency. Considering operational mode characterized by a consistent Hall component the higher the gyration frequency and the lower the collision frequency, the higher will be the amount of induced Hall current.

€

β = ωeτe (3)

Taking into account effects of the Hall parameter on thrust operation means to analyze his dependence on the magnetic field strength, pressure, and temperature. Defining the electron gyration, collisional frequency, electronic pressure respectively as (4) (5) (6) (7)

€ and considering the dependence of the conductivity on the electron temperature, the Hall parameter can be rearranged as follow (8)

Thus in order to increase the azimuthal flows following steps are required: •  Large magnetic fields •  low values of pressure, high electron temperature (nearly square dependence)

o  The difference between theoretical expected values of the Hall parameters (ranging between 10-100) and experimental evidences (azimuthal currents measurements) implies that the efficiency of the magnetic nozzle in the energy conversion is limited [5]

€

ωeτ e =σBene

∝BTe

5/2

pe (8)

€

ωe = eBme

(4)

€

ve = nee

2

σme (5)

€

ve = pee

2

kTeσme (7)

€

pe = nekTe (6)

Due to the different acceleration mechanisms involved in thrust generation:

•  A proper design of the magnetic field plays an essential role in the acceleration process

•  High values of ionization are required in order to ensure an appropriate degree of mass to electromagnetic effects (being mass involved in the specific impulse and the thrust generated trough electromagnetic effects)

•  Anomalous diffusion of electrons across the magnetic field as well as the presence of a non uniform azimuthally discharge have to be taking into account affecting operation of the thruster. [5] [6]

•  Geometry of the applied magnetic field affects operation parameters as discharge voltage V, anode voltage losses, electron density [6]

€

Γe = −Dednedr

−µeneE

€

E = −1ene

16 jeB + kTednedr

Considering the flux of electrons to the anode with the Bohm coefficient for the anomalous diffusion, and rearranging the Einstein relation as follows

€

De=Bohm =116

kBTeB

we obtain an expression for the electric field as function of he external applied field [6]

Results from both experimental campaign and theoretical efforts [1][4][6][14][15][16] show directions for changing the thruster geometry and to improve thruster performances:

•  Observed rapid increase in thruster performance with applied-field strength using a larger anode radii indicate that both larger anodes and increased magnetic fields should be adopted. [6]

•  Using both cathode and short anode yielded the highest measured performance due to the reduction of anode/electrode losses. [6]

•  Designing the anode and applied-field so that the field lines cross the anode surface* thus reducing the requirement for a high anode fall voltage, is believed also to reduce the anode power losses and increase thruster efficiency. [16]

*Has to be noticed that in regarding to the last point others authors point out to design the applied field line to be parallel to the anode surface in order to minimize anode losses [1]

SX3 design includes several of these features •  cathode to the anode radio is high if compared with similar class devices •  cathode is a recessed one and anode exhibit a short extension •  applied magnetic field in this case is shaped to be flattered to the anode surface

Instabilities & operational conditions

•  Definition of Instabilities and Onset related phenomena. •  How instabilities affects overall thruster performances?

Phenomenology: Onset is defined as a “collection of behaviours associated with a transition to large-amplitude terminal voltage fluctuations (hash), transients in plasma properties, and growth in anode fall voltages” once exceeded a certain value of a critical parameter k* (ratio between discharge current and mass flow rate) [16]

Effects: •  Limits the max achievable Isp •  Decrease in thrust efficiency (as anode losses increase) •  Electrode erosion (decreasing thruster lifetime) (1)

Effect of erosion on a McHc operated above the onset (quasi-steady regime)

(left) BoL (right) after 200 shots Alta AF-MPD 100kW [19]

Fig. (1)

Instabilities & operational conditions Current and Voltage fluctuactions at the Onset (2)

(Up) Discharge Current: Amplitude: 600-900 [A] ≈ 20% Im* (Down) Discharge Voltage: Amplitude 16-21 [V] Sampling Frequency: 0.5 [ms]

Discharge current I [A]

750

MFR [mg/s] 100

B** [T] 0.1

Ra [mm] 38

Rc [mm] 6.4

NASA-Lewis AF-MPDT 100 kW class Configuration I Water cooled Cu anode W-2%Th alloy cathode

** Applied magnetic field B measured at the centerline of the cathode tip

* Mean value of discharge current (2)

Anode starvation [4][10] •  Diffuse current conduction to the anode

is sheath-limited •  reversal in the sign of the anode sheath

as the driven current increase cause a drop in the density of charge carriers near the anode

•  anode can no longer collect the total current imposed by the external source

•  current conduction turns to discrete anode spots, implying local anode vaporization

Plasma Instabilities •  drift instabilities, excited by large relative

velocities between electrons and ions •  Micro instabilities (GLHDI, ECDI, space

charge instabilities) [11][12][13] •  Macro instabilities (MHD kink instabilities)

[2][3]

Formulated Theories for the Onset riddle explanation:

Effect of the back EMF [8] •  Increasing of the current to mass flow

ratio leads to it is possible for the accelerator plasma to flow quickly enough to impede current from flowing between the electrodes instabilities)

Instabilities & operational conditions

•  k* onset parameter •  operated current, ionization current ratio •  current ratio for SF and AF according to

Tikhonov •  Tikhonov parameter for SF and AF-MPD

€

k* = ( I2

˙ m , I2

˙ m Mion

)

ξ =IIci

ξTSF =

IIcrit

SF ξTAF =

IIcrit

AF

AoSF =

µoγI2

4πao ˙ m Ao

AF =(Ra − Rc )(Bself + Bext )I

4πao ˙ m Definition:

•  Classic onset parameter is defined as the ratio between current and mass flow rate. •  Influence of the atomic mass of the propellant has been verified by several authors [4] •  Ratio between operated and ionization current measures the edge over critical conditions [4] •  Tikhonov parameter Ao represents the ratio between the gas-dynamic and magnetic

pressure. The eq. in the case AF-MPDT, has been developed empirically, still capturing relevant trends of operated parameters. [1]

Instabilities & operational conditions

Parameters used to define Critical Regimes:

•  Tikhonov criterion for AF-MPDTs •  General theoretical formulation is based upon the analysis of the ideal MHD channel •  In the AF-MPDT case the Tikhonov parameter links different operational parameters:

applied magnetic field, mass flow rate, discharge current. •  The computed value is compared with a geometric parameter, function of the

thruster geometry in terms of anode and cathode radii •  Equating these two parameters allows to determine different critical conditions

€

AoAF ≤ Ao

geoStability condition:

€

Ao = f (Bext , Bself , ˙ m , I , R , ao)Bext = f (I) parametric ˙ m Bext = f ( ˙ m ) parametric I

Equivalent representations

€

AoAF =

(Ra − Rc )(Bself + Bext )I4πao ˙ m

€

Aogeo =

3.6Ra

Rc

−12

(3) Comparison of Tikhonov geometric parameter and operated conditions for different AF-MPDs thrusters

Considerations: o  Arrows indicates thruster operated in critical conditions or above it o  When not clearly expressed critical conditions are assumed by the analysis of available

voltage/current diagrams o  Two types of thruster clearly operated safely even in conditions in which Tikhonov

criterion provides indications of unstable behaviours occurrence o  Both Tohuku University and SX3 AF-MPDTs are characterized by relatively much higher

slender magnetic field geometry w.r.t. others thrusters o  Differences in the SX3 operated conditions for the 2012 and 2013 campaigns only

depend on a different magnetic field geometry

Summary of geometric and operational characteristic of analyzed AF-MPDs thrusters

Influence of Temperature & Ion sound velocity

•  In the general formulation by Tikhonov the ion sound velocity is computed assuming the same temperature for both ions and electrons.

•  Values of ion sound velocity depend on the the atomic mass of the propellant •  politropic constant is usually assumed to be close to the value for ideal gases,

(5/3)

however

•  several Japanese authors [20] dropped off the assumptions of an equal politropic constant and temperature for both electrons and ions in relation to the very peculiar operated conditions of high power (MW order), high mass flow rate, high applied magnetic field with different propellant (He). ( Te ≈ 4-5 [eV] )

•  Temperature measurements performed at Alta with HpT ranges between 3-4 [eV] without applied magnetic field up to 9 [eV] when an external field is applied [4]

•  Original measurements of Tikhonov group range between 2-3 [eV] for electron temperature at the cathode tip.

•  Work of Myers at NASA-Lewis center shows electron temperature ranging from 1 [eV] to 2 [eV] exhibiting a trend clearly related to that one of the electron number density w.r.t. the radius of electrodes gap. [6]

•  Computation of Ion sound velocity

Influence of Ion sound velocity on the Admissible current €

ao =γkTeMi

W i t h i n t h e a s s ump t i o n o f a n e q u a l t e m p e r a t u r e f o r b o t h e l e c t r o n s a n d i o n s a n d a s sum i ng t h e ad i a ba t i c i n de x v a l u e f o r p e r f e c t g a s e s , t h e i o n s o u n d v e l o c i t y r e d u c e s to eq. (I)

Ao Tikhonov parameter can be compu t ed a s f u n c t i o n o f t h e I o n s o u n d v e l o c i t y : e q u a t i n g t h i s v a l u e t o t h e g e om e t r i c p a r a m e t e r l e a d s t o a representation of the admissible current as function of Te.

Admissible current increases as Te increases

Effect of electron temperature variations are more relevant as the mass flow rate increases

€

k = Boltzmann constant

€

Te = electron temperature ≈ 2.5 [eV]

€

Mi = propellant atomic weitgh

€

γ = 53 = adiabatic index

(I)

Ra [mm] 43 Discharge current, I [A] 450 max

Rc [mm] 6 MFR [mg/s] 20

RcII* [mm] 12 Applied magnetic field, B [T] 0.1

•  Analysis of the SX3 case: •  SX3 has been operated at IRS in the 2012 and 2013 with different operational

parameters •  A complete new magnetic flux density geometry has been implemented in last exp

campaign, trough the usage of a new designed set of coils. •  This modification results in a drastic improvements of performances: during the

2012 exp campaign the SX3 has been operated at current levels up to 400 [A], [14] •  In comparison previous experimental campaign achieved operations up to 225 [A] at

which the probable occurrence of instability [15]

SX3 Geometric features Operated conditions

*RcII: Alternative cathode, not implemented yet

Exp campaign analysis (2012)

•  Constrained represents the relation between applied magnetic field and discharge current for parametric values of mass flow rate at critical conditions.

•  For a given value of mass flow rate increasing discharge current implies to operate at lower value of applied magnetic field

•  This trend is more evident at low values of mass flow r a t e a n d d i s c h a r g e currents

•  Tikhonov criterion underestimates admissible current at given operated conditions of mass flow rate, applied magnetic field

•  Considering the I=200 [A] measurement the predicted value of Tikhonov critical current (lower curve) is about 80 [A] lower than the operated condition

€

Ao = f (Bext , Bself , ˙ m , I , R , ao)Bext = f (I) parametric ˙ m

€

R ≅ 7.12ao ≅ 2500 [m/s]

Trends:

•  Increasing mass flow rate allows to operate at higher values of discharge current for any given value of applied magnetic field

•  Curves represents the same parametric formulation for different cathode radii, respectively Rc = 9 [mm] (up) and Rc = 12 [mm] (down)

•  Anode to cathode ratio is a critical parameter, an increasing of this ratio leads to higher value of admissible current

•  As the external magnetic field increases, lower values of current are permitted

•  Effect of increasing the anode to cathode ratio also affects the trends of parametric curves: an increasing of mass flow rate is more effective in order to operate at higher current conditions if applied for higher anode to cathode radii

•  Is worth to notice that operated conditions with the SX3 in 2012 correspond to a Tikhonov criterion applied to a lower anode to cathode ratio

€

R ≅ 4.78

€

R ≅ 3.58

€

Ao = f (Bext , Bself , ˙ m , I , R , ao)I = f ( ˙ m ) parametric Bext

€

R ≅ 7.12ao ≅ 2500 [m/s]

€

R ≅ 5

€

R ≅ 3.58

Trends:

•  Curves represent the same paramet r i c fo rmu la t ion fo r d i f f e r e n t c a t h o d e r a d i i , respectively Rc = 9 [mm] (up) and Rc = 12 [mm] (down)

•  Effect of increasing applied magnetic field on values of critical current is higher for lower values of the magnetic field itself

•  As the applied magnetic field inc reases above va lues o f 0.3-0.35 [T] the effect in terms of reduction of admissible current decreases (this tendency is highlighted by the decreasing in the values of curves slope with increasing magnetic field)

•  The effect of a reduction in the admissible current as the applied f i e l d i n c r e a s e s , i s l e s s pronounced as the anode to cathode ratio increases

•  Even in this case operated condition of the SX3 correspond to a Tikhonov criterion applied to a anode to cathode ratio equal to R = 5

Trends:

• Curves in graph (1) summarized trends of the discharge current as function of the mass flow rate for parametric values of magnetic field and for 3 different values of anode to cathode radius ratio (R=7.12 - 4.78 – 3.58) • Effects of a reduction of the anode to cathode radius are nearly equivalent to an increasing in the applied magnetic field.

• Curves in graph (2) represent the applied magnetic field Vs discharge current relation in critical conditions for the ZT1 thruster case. • The ZT1 operated in safety regime with no occurrence of instability. • Tikhonov criterion correctly predict critical conditions above the operated one. • Has to be pointed out that ZT1 has an anode to cathode ratio R=5.34: from this and previous considerations is argued that Tikhonov criterion validity is s t rong l y a f f e c t ed by the anode to cathode ratio. • This characteristic also suggests a way to co r r ec t the T i khonov criterion at high values of R

(1)

(2)

•  Kruskal-Shafranov criterion is based on a model describing a typical instability mode that may arise in several confined plasmas geometries (fusion devices, z-machines, plasma guns)

•  such as configurations (i.e. Tokomak) are potentially unstable to the current driven external kink instability

•  The kink stability of a cylindrical magnetic plasma column is often quantified in terms of the so-called “safety factor,” q

•  The safety factor measures the pitch of the magnetic field lines as they helically wind around the axis of the plasma column.

•  If the field line pitch becomes too steep (q becomes too low), the flux rope will kink in response to long-wavelength magnetic perturbations. The onset of the most dangerous kink mode, the external kink, depends theoretically only on the value of the “edge” safety factor”

Different geometries have been object of study with this criterion in several fields (fusion devices, solar coronal simulation, MHD converters)

•  toroidal geometries (Tokamak configuration) (I) •  line-tied partial-toroidal (plasma column held fixed at both ends) (II) •  open-end geometries (such as AF-MPDTs) (III)

I II III

Among the very large amount of literature currently available on the topic a list of works focused on the analysis of the Kruskal-Shafranov limit is also reported in the following [18]

Modelling of instabilities with Kruskal-Shafranov limit: Experimental and theoretical efforts

Kruskal-Shafranov limit has been extensively used in several studies aimed to detect and identify instabilities in AF-MPDTs [2] [3] and later also in SF-MPDTs [22]

•  Experimental activities at Alta firstly attempted to modelize the instabilities occurrence with the Kruskal-Shafranov limit

•  The campaign consisted in both electrostatic and magnetostatic measurements of voltage, discharge current, azimuthal and axial magnetic field.

•  A Fourier analysis of the signals allowed to detect a regular oscillation of 100 kHz in both electrostatic and magnetic output.

•  This picture is consistent with an azimuthal propagation of the kink mode. •  A direct correlation between energy modes* of the kink and operational parameter

has been investigated, specifically w.r.t. discharge current I and applied magnetic field B

•  A correlation between the energy modes and the critical current threshold computed using the Tikhonov criterion has been identified.

*As widely know definition of energy modes m,n are referred to the expression of the expansion of cylindrical displacement of the plasma column in perturbation analysis. (See for example [17] [18])

Summary of the experimental and theoretical results achieved at Alta:

•  Kink mode instabilities have been observed in several exp campaign at Alta •  This kind of external mode instabilities are considered as the principal cause of

the occurrence of Instabilities and Onset behaviours in the AF-MPDs thruster •  Development of m=0 and m=1 modes is believed to cause lower efficiency

operated conditions above the Onset

Kruskal-Shafranov limit and current regime: on the applicability on the SX3 case

•  Alta experimental campaign involved at least three AF-MPDTs design; HpT, MAI Type, and a conventional single hollow cathode design [21]

•  HpT and MAI Type especially follow a so called HCMM “high current approach” in comparison with standard pursed DLR/IRS approach based on LCHM “high magnetic flux low current” [15]

...is the kink mode instability hypothesis applicable to the SX3 operational regime?

Have to be noticed that as the Alta design thrusters are characterized by an high discharge current design, the MFR (mass flow rate) used is also much higher and ranging between 100 and 660 [mg/s] for the HpT and up to 100 [mgr/s] for the other cases [3] so in the best case at least 5 times the operated MFR currently experienced with the SX3

Summary of the experimental and theoretical results achieved at Alta:

•  Kink mode instabilities have been observed in several exp campaigns at Alta •  This kind of external mode instabilities are considered as the principal cause of the

occurrence of Instabilities and Onset behaviour in the AF-MPDs thruster [2] •  Mode m=0 and m=1 are modes considered as responsible of lower efficiency operation

above the critical regime •  Modes energy is negligible if Itot < Icrit •  Modes energy increase as the I-V characteristic of the discharge becomes critical •  Axial plasma wavelength represents the characteristic length of the kink, and is verified

to be comparable with the length of thruster plume L •  Instability mode is regarded as a m/n = 1 helical kink mode

Time [ms] 0 3 0 Bz [T] 0.1

Voltage & Current characteristic

Power Spectrum of the Voltage signal at critical conditions

Axial wavelength Vs Bz

V-I characteristic and critical current threshold

Safety factor condition at resonant surface of radius a

Safety factor considered as function of inverse pinch radius

€

2πR0 = L€

q =2π

µ(r)L≥1

Kruskal-Shafranov condition for stability

€

q(a) ≥1

Definition of relevant parameters:

•  Safety factor q •  Inverse pitch of magnetic field line

•  Starting from the Kruskal-Shafranov limit in the case of a toroidal configuration a safety factor q can be expressed for an open-end case: the inverse pitch is considered as the ratio between the axial current and the magnetic flux

•  From this formulation an admissible current value can be establish as follow [3]:

€

µ =µ0Iψ

=µ0Iz (r)Bz(r)A

=µ0IBzπr

2

€

q =2π

µ(r)L=4πr2Bz

µ0IzL≥1

€

Iz ≤(2πr)2Bz

µ0L€

q(r) =rBz (r)Bθ (r)

=1

µ(r)R0

€

q =2πrBz(r)LBθ (r)

=2π

µ(r)L=1

1

2

3

4

€

2πR0 = L

Admissible current

•  Following parameters are defined as in figure (k)

•  Plasma column length L is proportional to the extension of the plume. [4]

•  Assumed values for L have been computed considering the Tikhonov correlation between plume extension and Ra at a given applied magnetic field B

•  Radius r is assumed equal to the cathode radius Rc

•  Constant axial magnetic field Bz •  Axial current Iz, constant along the z axis

over the cathode surface tip, represents the overall discharge current

L represents the characteristic length of the kink[3] Exp camapign assests that the kink originates at the cathode tip and exhibit an initial radial extension comparable with the cathode dimension [2] Constant applied magnetic field

€

L = (2 ÷ 3.5)Da

€

Bz ≈ Bext = 0.1

€

r ≈ Rc

Parameters meaning

Fig. (k)

•  Influence of plasma column length L on critical current I computation

•  Influence of plasma column radius r •  Influence of magnetic field strength

•  An increase of the plasma column radius r leads to higher values of admissible current

•  Assuming a longer plasma column length L decrease the value of admissible current

•  Computed results for the SX3 represent the lower and upper limit of the admiss ib le current for different va lues o f p lasma column length

•  For L ranging from 2 t o 3Da e x p e c t e d critical current for the kink mode instability ranges from 550 to 650 A

•  Within the Taylor theory (time decay of magnetic helicity longer than the time decay of magnetic energy) magnetic field can be modelized as Bessel Functions (begin solution of Ampere law in these states) [18]

•  This modelization gives an indication of the fraction of the induced magnetic field as function of radial direction for parametric values of L

•  According to this model in the SX3 case induced values of axial magnetic field are negligible w.r.t. the external applied magnetic field for a wide range of operational parameters

•  Theoretical value of inverse pinch as function of the plasma column length is represented in the following graph (1)

•  Expected values of experimental inverse pinch parameter are plotted Vs the plasma column length

•  Assuming L ranging between 2 and 3Da different values of inverse pinch parameter can be computed

•  Each of the results correspond to a certain value of admissible current

€

µ =4πL

€

µ =µ0Iψ

ψ = πr2Bz

(1)

Results:

•  Critical current values with Tikhonov criterion for instability are underestimated

•  Kruskal-Shafranov limit predicts critical current values between 550 and 650 [A] for the analyzed conditions

•  Strongly influence of the magnetic field geometry on the admissible current for the SX3 is evident from the analysis with Tikhonov criterion

•  At low current regime magnetic field geometry seems to be the most important parameter to affect thruster functioning if compared for instance with variations in the mass flow rate

Currently ongoing activities:

•  Criteria for “magnetic field topology similarity”: aimed to determine comparable operational conditions w.r.t. magnetic field topology between different thruster geometries (electrodes radii)

•  Preliminary consideration on a future experimental campaign related to Instabilities investigation: aims, hardware availability, feasibility, expected outcomes

•  Consideration about Ionization current formulation for AFMPD thrusters

Similarity of magnetic field topology between 2 different configurations is crucial for:

•  Instabilities behaviors: arc c u r r e n t s p a t t e r n s a n d discharge voltage are strongly affected by the magnetic field geometry and strength

•  Thrust, efficiency: theoretical determination and verification of those parameters depends g r e a t l y o n p r o p e r characterization of magnetic field in the plume

•  Possible future caharcterization of discharge plume (electron temperatue, particle number density)

How to compare different geometric configurations? (different electrodes geometries)

Comparison of divergence of magnetic field lines at Anode and Cathode reference points

€

αA ,z

€

αA ,B

€

αC ,B

€

αA ,z =

€

αA ,B =

€

αC ,B =

angle between anode surface and magnetic field line

angle between anode magnetic field line and z axis

angle between cathode magnetic field line and z axis

Simply analysis of magnetic field geometry performed with FEEM software includes the study of an additional Inner magnetic coil in order to achieve same similarity condition for different configurations.

Following examples in figures are related to the analysis with the current Outer coil set up, operated with the following parameters:

SX3 Outer Coil (71 turns)

Total current = 452 Amps → Ba = 0.1 T Voltage Drop = 8.83697 Volts Flux Linkage = 0.940809 Webers Flux/Current = 0.00208144 Henries Voltage/Current = 0.0195508 Ohms Power = 3994.31 Watts

Configuration 1: Ra = 32.25 mm, Rc = 12 mm

Configuration 2: Ra = 43 mm, Rc = 12 mm

Ana l y s i s w i t h FEEM a l l ows to determine also others figures of merit for a given coil set up such as:

mean value of magnetic flux density across anode surface,

average value of magnetic field for a given length

power consumption of operated coil set up

The definition of a feasible experimental campaign requires the identification of:

•  Instruments available at IRS •  Variables that can be measured •  Timing and set-up feasibility

Alternative I Voltage & currents measurements: Aimed to:

•  Assessment of predicted critical condition with the Kruskal-Shafranov limit •  Indications for a modified Tikhonov criterion** •  Assessment of the effect of magnetic field strength and geometry on critical current •  Analysis of voltage spectrum in order to identify a dominant frequency peak

Possible hardware requirement for the electrostatic set-up (Voltage – Discharge current signals)

•  Required bandwidth up to 500 kHz •  Acquisition sampling frequency up to 10 MHz

**See “Current ongoing activities” in the previous.

Alternative II (In addition to exp measurements at point II) Optical measurements of Electron temperature, plume length, plume oscillations

Aimed to: •  Determination of plume characteristic •  Analysis of emitted spectrum line in order to assess the presence of single, doubled

ionized charge ions •  Assessment of the presence of spectral lines associated with the sputtering emission

from electrodes in critical conditions •  Confrontation of Te with assumed values of temperature with Tikhonov criterion •  Analysis of brightness spectrum in order to verify the existence of dominant frequencies

a)  Note: Previous exp campaign has been already focused on measurements of voltage, current, thrust, so in the following only some hints about the spectroscopy analysis are provided

Emission Spectroscopy set-up

•  Hardware: •  Spectrometer •  Collimator •  neutral filter •  data recording & post process

Methods & Constraints

•  Identification of a suitable centerline-average emitted intensity •  Assessment of required parameters (intensity ratio resolution, wavelength range) •  Model and assumption for the computation of the electron temperature (es. relative line intensities approach) •  Spectrometer calibration •  Corrections (transmittance of the medium)

Vielen Dank für Ihre freundliche Aufmerksamkeit.

[1] Research of Plasma acceleration processes in self-field and applied magnetic field thruster, V.B. Tikhonov, S.A. Semenihin, RIAME, Moscow, IEPC, 1993

[2] Further Experimental Evidences of the Development of Kink Instabilities in MPD Thrusters, F. Paganucci, M. Andrenucci, M. Agostini, et al. Centrospazio-ALTA, Consorzio RFX, ENEA - Joint Propulsion Conference and Exhibit, (2005)

[3] Critical regimes and magnetohydrodynamic instabilities in a magneto-plasma-dynamic thruster, M. Andrenucci, F. Paganucci, and P. Rossetti Department of Aerospace Engineering, University of Pisa, and Centrospazio, V. Antoni and M. Bagatin Consorzio RFX, PHYSICS OF PLASMAS (2004)

[4] A critical review of the State-of-the-Art in the performances of AF-MPDs, A.D. Kodys and E.Y. Choueiri, Joint Propulsion Conference Acts, (2005)

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