Suppression of Kink Instability in Magneto-Plasma-Dynamic Thrusters

M. Zuin¤, R. Cavazzana¤, E. Martines¤, G. Serianni¤, V. Antoni¤, M. Andrenucci†,¤¤,
F. Paganucci†,¤¤, P. Rossetti† and M. Signori†
¤Consorzio RFX, Associazione EURATOM-ENEA sulla fusione, corso Stati Uniti 4, 35127 Padova, Italy
†Alta-Centrospazio, Via A. Gherardesca 5, 56014 Pisa, Italy
¤¤Department of Aerospace Engineering, University of Pisa, Italy
Abstract. The suppression of helical kink mode in a Magneto-Plasma-Dynamic thruster for space propulsion has been
successfully obtained by interrupting the helical current components associated to the spontaneous distortion of the plasma
column. The plasma is driven from a largely fluctuating to a quasi-quiescent state, characterised by a tremendous reduction of
electrostatic and magnetic field fluctuation levels. As a consequence a significant reduction of the power required to sustain
the plasma current is observed, along with thruster efficiency enhancement. This result, while confirming that power losses
are largely induced by plasma instabilities, opens up new scenarios for the use of this kind of thrusters as primary propulsive
systems in long-term space missions.
Keywords: plasma instability, kink, thruster, instability control
PACS: 52.75.Di, 52.25.Xz, 52.35.Py, 52.70.Ds
Magneto-Plasma-Dynamic (MPD) thrusters are space propulsion devices, which operate as electromagnetic plasma
accelerators and constitute a high electric propulsion candidate for space missions, ranging from orbit raising to
interplanetary manned and/or cargo missions of large spacecraft [1]. The acceleration is induced by the interaction
between a current, driven by a potential difference between an anode and a cathode, and a magnetic field, which
can be a combination of a self-induced (i.e. produced by the plasma current itself) and an externally applied one.
When driven to operate at plasma currents above a threshold value, MPD thrusters have shown a degradation of their
performance, in terms of thrust efficiency, associated to the so called ’onset’ phenomenon, characterized by large
fluctuations of the electrodes and the electromagnetic plasma signals [2, 3]. Recent experimental investigations have
shown that such fluctuations are induced by the development of large-scale magneto-hydrodynamicMHD instabilities,
with the features of helical kink modes, due to a violation of an MHD stability criterion [4, 5]. These instabilities are
indeed responsible for the large increase of the electric power losses beyond the onset condition. In this work a first
successful attempt aimed at controlling these instabilities and the effect of the kink mode suppression on the global
properties (thrust and power balance) are presented.

In Fig. 1 a scheme of the MPD thruster under investigation is shown. A cylindrical system of coordinates is
introduced, with r = 0 placed on the thruster axis, the z-axis taken to point in the outward direction with z = 0 at the
thruster outlet. A copper hollow cathode, 20 mm in diameter, is located in the inner region of an insulating conically
shaped support (see Fig. 1), while the anode consists of a copper ring, 200 mm in diameter, placed at z=0. The electric
power is supplied to the thruster by a Pulse Forming Network (PFN), configured to give quasi-steady current pulses
(Idis) lasting 2.5 ms, ranging from 3 to 7 kA. The neutral gas is injected in the hollow cathode by means of fast acting
solenoid valves. The discharge takes place when a steady state mass flow rate is reached (t =0). As working gas, argon
has been used at mass flow rate m˙ ranging from 120 to 400 mg/s. The thruster has been operated in applied-field MPD
configuration, with a quasi-steady axial magnetic field (Bext ), produced by an external coil (shown in Fig. 1), ranging
from 40 to 100 mT on the thruster axis. The thruster has been mounted on a thrust stand inside a cylindrical vacuum
chamber (length = 3.5 m, radius = 0.6 m), which allows to maintain a back pressure of the order of 10−2 Pa during
the pulse. The thruster electrodes are floating with respect to ground, in order to avoid secondary discharges involving
the vacuum chamber, so that the discharge voltage (DV) is obtained by subtracting the cathode voltage signal from the
anode voltage signal [3].
Typical plasma parameters measured in the thruster are ne ¼ 1020m−3 and Te ¼ 5−10 eV [6]. The Alfvén time is
of a few ms, while the plasma resistive diffusion time is of the order of 100 ms.
Several arrays of probes arranged in azimuthal and radial direction have been used, in order to characterize spatiotemporal
properties of plasma fluctuations. Two azimuthal arrays of 4 equally spaced bi-axial magnetic coils, each
measuring Bq and Bz fluctuations, were located in the inter-electrode region, one at z = −109 mm the other one at
z = −150 mm, on the inner surface of the supporting insulating cone, as is shown in Fig. 1. An azimuthal array, 41
mm in radius, of 8 equally spaced electrostatic Langmuir probes, measuring the floating potential was placed at z = 0,
where also a linear array of 21 magnetic coils has been mounted, alternatively measuring Bq and Bz fluctuations,
covering the full anode radius. The bandwidth for the measurements is estimated up to 1 MHz.

Typical discharge waveforms of plasma current Idis, applied voltage between anode and cathode DV, and a signal
from one of the magnetic probes of the azimuthal array, measuring Bq fluctuations, are shown in Fig. 2 (left), for a
condition beyond the onset threshold, i.e with a largely developed kink mode. The magnetic measurements exhibit a
high level of fluctuations during the discharge, superposed to the average level of the magnetic field induced by the
plasma current itself. Such oscillations have a regular behaviour at a frequency of about 70 kHz, as can be deduced
by the expanded time-window in Fig. 2, and are present in the electrostatic component of plasma fluctuations as
well. The different azimuthal periodicities have been discriminated by Fourier-decomposing the signals from the
azimuthal arrays. A strong m = 1 nature of the fluctuations has been found, as can be seen in Fig. 2 (right), showing
the time behaviour of m = 0 and m = 1 modes. This result is in good agreement with what observed on MPD thrusters
with different geometry by means of electromagnetic diagnostics [4], and, more recently, by means of 3D Ultraviolet
tomography, which showed an emissive helical structure, with m = 1 azimuthal periodicity, non-uniform in the axial
direction, rotating when Bext is applied [7]. In Fig. 2 (right), the phase of the m = 1 mode estimated from the signals of
the two arrays in different axial positions (Dz = 41 mm) is also plotted. A phase shift between the two axial positions
is measured, corresponding to a time delay Dt of about 3 ms. In terms of the helical structure of the mode, this
corresponds, at 70 kHz, to an estimated axial wavelength lz (= f −1Dz/Dt, where f is the rotation frequency) of the
mode of » 20 cm, comparable to the axial system dimension.
On the basis of the experimental observations, a technique to reduce the negative effects of the kink is here proposed,
based on the idea of dividing the discharge into two halves by means of an insulating plate, which intercepts the
azimuthal current components associated to the helical deformation of the plasma column. The plate has been placed
into the inter-electrode region, extending in the (r, z) plane, covering the full radius of the insulating support, axially
extending from the cathode tip to the anode, as shown in Fig. 1.

FIGURE 3. Left: temporal evolution of a floating potential (Vf ) signal taken at z = 0, r = 41 mm: a) standard MPD configuration,
b) with insulating plate inserted (Idis = 7 kA in this case). Right: Azimuthal m = 0 and m = 1 mode amplitude (normalized to the
value of the azimuthal magnetic field at the edge of the plasma column Bq (a)) plotted as a function of the total plasma current Idis
without and with (full circles) effective kink suppression (m˙ = 400 mg/s; Bext = 40 mT in all these cases).
Fig. 3 (left) compares one of the floating potential signals measured in the same thruster operating condition (Idis,
m˙ and Bext ) with and without the proposed geometry modification. The most evident effect of the inserted plate is to
strongly reduce high frequency potential fluctuations, without significantly modifying the slow trend during the quasistationary
phase of the discharge, which appears after a transient initial period, lasting less than 0.4 ms. The insulating
plate has a tremendous effect on the magnetic fluctuations as well, as can be observed in Fig. 3 (right), where the
m = 1 and m = 0 mode amplitudes, averaged over 1 ms during the discharge, are shown at different current regimes,
both in the standard and in the modified MPD configuration. The m = 1 mode amplitude strongly increases with Idis in
standard operating conditions (the threshold current value for the onset of the kink mode is between 3 and 4 kA for the
experimental condition shown in Fig. 3 right), while in the new configuration negligible magnetic fluctuation energy
is observed at all the explored current regimes.
From the electrical characteristics (Idis vs. DV curve) of the discharge in the two conditions it can be deduced
the effect of plasma instability suppression on the discharge global properties (Fig. 4 left). The two Idis vs. DV curves
almost coincide at low current levels (below 3 kA), when the amplitude of the mode is small also in standard condition,
while a large reduction of the applied voltage, about 30% of the maximum value, can be seen at higher current levels
when the kink mode is suppressed.
The effect of the kink suppression on the discharge equilibrium can be better understood by analysing of the radial
profiles of Bq and Bz components of the magnetic field (Fig. 4 right), measured by the radial array of magnetic coils
at the thruster outlet. Bz values have been evaluated as Bext +Bcoils
z , as the Bcoils
z values, measured by the magnetic
pick-up coils, cannot include Bext , which is in a stationary condition when the probe sampling starts.
A large paramagnetic generation of axial magnetic field is observed in the presence of the kink. When the kink
controller is applied, this effect almost disappears (see Fig. 4a).
In particular, lower Bz values are measured by the magnetic coils close to the thruster axis, with the resultant Bz
profile closely resembling the unperturbed Bext . In the Bq profile no clear modification is observed, which means that
the Jz distribution is only weakly affected in the new plasma configuration.
As the thrust, T, inMPD thrusters is mainly produced by the Lorentz force Jr×Bq , where Jr is the radial component
of the discharge current flowing from the anode to the cathode, any modification of current distribution implies,
in principle, a change in the thruster performance. A ballistic measurement of the impulse levels produced.

thruster has been thus performed [3], in order to study the effect of the insulating plate on MPD thrust efficiency hT
(hT = Pth/Ptot , where Pth = T2/2m˙ is the thrust power and Ptot = DV · Idis is the total electric power supplied to the
thruster). It is found that the modification of device geometry configuration does not imply significant changes of the
thrust performance, as no variation of the impulse has been measured on the thrust stand when the insulating plate is
inserted. This means that, in the case of effective instability suppression, the same thrust is obtained at a given plasma
current, but with lower applied voltage, i.e. lower total electric power, with a significant improvement, about 30%, of
the thrust efficiency.
It is moreover interesting to note that at the highest current levels, though mode amplitude tends to decrease (Fig. 3
right), the improvement is less pronounced. This result can be related to the previous experimental observation that at
high current conditions the kink is stretched towards the outer plume region (at z > 0) [4], where the insulating plate
is not present (see Fig. 1), which makes it probably less effective in suppressing the mode in the all plasma volume.
This suggests that, in the future, a proper modification of the geometry of the insulating plate could result in a further
improvement of the thruster efficiency.
FIGURE 4. Left: applied voltage DV plotted as a function of the total plasma current Idis without and with (full circles) effective
kink suppression. Error bars come from averaging over different shots (m˙ = 400 mg/s; Bext = 40 mT). Right: experimental radial Bz
(a) and Bq (b) profiles measured at z = 0, without and with (full circles) effective kink suppression. Dashed-dotted line is the radial
profile for the unperturbed z-component of Bext .
In conclusion, a successful attempt to control large scale MHD instabilities in the plasma produced by a MPD
thruster for space applications by a simple passive method has been presented. It has been shown that the suppression
of the helical m=1 kink mode, which, in the past, had been proven to be associated to the so-called onset phenomenon,
responsible for thruster performance degradation at high current regimes, drives this kind of plasmas to a quiet state
characterized by negligibly small magnetic and electrostatic fluctuations. The final effect of the induced plasma
instability damping is a an improvement of the MPD thruster efficiency, due to a significant power loss reduction,
so that the relationship between kink development and power balance in plasma columns is further confirmed. The
proposed technique, though intended to be only a proof of principle, demonstrates that it is possible to safely drive
MPD thrusters to operate at high current regimes and opens up new perspectives for their development and future use
in long-distance space missions.
REFERENCES
1. R. G. Jahn, Physics of Electric Propulsion, (McGraw-Hill, New York 1968).
2. A. P. Shubin, Sov. J. Plasma Phys. 2, 18 (1976)
3. F. Paganucci et al., IEPC-01-132, 27th International Electric Propulsion Conference, Pasadena, USA, 2001.
4. M. Zuin et al., Phys. Rev. Lett. 92, 225003 (2004).
5. J. P. Freidberg, Ideal Magnetohydrodynamics, Plenum Press, New York (1987).
6. M. Andrenucci et al., IEPC-03-0301, 28th International Electric Propulsion Conference, Toulouse, France, 2003.
7. F. Bonomo et al., Phys. Plasmas 11, 4761 (2004).

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