Automatic Sub-Microwave Measurements on a Beam-PlasmaExperiment

Pedro Francisco de Deus Lourenço

Engineering PhysicsInstituto Superior Técnico - Universidade de Lisboa

October 2015

Abstract

Beam-Plasma interaction apparatuses, developed between the 1960s and the 1980s, were used to studythe underlying mechanisms of low temperature plasmas and wave propagation. In today’s science, thesecan provide an unique environment to perform advanced experimental works on plasma physics. Theapparatus used was the Beam-Plasma experimental apparatus from IPFN, IST.

An initial maintenance and inspection process was conducted on the device to understand the physicalmechanisms behind operation. Then, this insight was used to design and implement a CODAC systemwhich was successfully used to operate the apparatus and acquire the experimental data, guaranteeingconditions of reproducibility for the operating conditions and parameters of the experiment. The CO-DAC hardware was made compliant with e-lab, allowing for a future integration under this platformand ultimately leading to the possibility of complete remote operation.

Two diagnostic techniques, resonant cavity and interferometry, were used to determine the param-eters of the plasma column. For a confinement field of 10.8±0.5mT, pressure of 3.0±0.1×10−2mbarand electron beam current of 18.0±0.5mA, it was possible to reconstruct the dispersion relation forfrequencies below the plasma frequency using interferometry. The technique allowed the determinationof the plasma frequency at 200±1MHz and the transverse wavenumber of 0.91±0.03 cm−1, thus witha density of 5.0±0.1×108cm−3. Under the same conditions, the density determined with resonant cav-ity was 3.3±0.9×109cm−3, thus one magnitude above. This discrepancy was attributed to the plasmacolumn radius considered inside the cavity and to the pressure gradient created inside the interactionchamber by the vacuum pump.

Introduction

The scientific work developed by several authorsover the years has given considerable insight overthe phenomena that govern low density plasmas.Today, more complex experimental setups are usedto study the behavior of plasmas under other work-ing regimes. Nevertheless, the contribution of thebeam-plasma experiment to today’s science is notover.

The beam-plasma provides fundamental insightto the study of plasma physics and slow wave propa-gation. It allows direct contact with an experimen-tal setup that creates a low-pressure and weaklyionized plasma in a user controlled environment,equipped with data acquisition systems. The po-

tential presented by this machine is now limited dueto the age of the mentioned systems. Moreover, theoperation of the machine is complex due to fluctua-tions in the experimental parameters that, with thepresent control system, make it difficult to attainoperation regimes in steady-state.

In order to solve this impairment, it becomesclear that an overall maintenance and upgrade mustbe conducted so the machine becomes compliantwith the most recent state of the art control anddata acquisition technologies. Thus, it becomespossible to achieve reproducibility for the operat-ing conditions and parameters of the machine andperform advanced experimental works on plasmaphysics. To do so, one must evaluate which op-tions may be more suitable to rebuild the machine

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structure, control and data acquisition systems, al-lowing a more recent and user friendly interface toreplace the current one.

Experimental Set-upThe cross-sectional schematic of the experimental

set-up core can be found on Figure 1. The experi-ment is made on a cylindrical interaction chamberwith a diameter of 8cm and a length of 75cm[1].The low pressure on the system is achieved throughtwo vacuum pumps, a first stage rotary pump anda turbo pump to achieve background pressures inthe order of 10−6mbar. The chamber is filled withHelium until the final pressure is around 10−4mbar.A vacuum gauge is connected to the chamber andallows to read pressure values.

The electron beam is produced by an incandes-cent filament[2] in Pierce configuration[1], locatedon the left side of the machine, while the axial con-finement is provided by 10 coils placed along thechamber. These produce an homogeneous magneticfield (within 1%) with values around 0.01T[1].

At the right end of the chamber is placed an elec-trostatic energy analyzer, aligned with the beamand machine axis. The energy of the beam istypically in the order of 2keV, 10mA and 4mmdiameter[1]. The experiment has a resonant electro-magnetic cavity for density measurements. Thereare also one movable and several fixed Langmuirpin probes along the interaction chamber[1].

Review of Main PublicationsSeveral works have been published regarding re-

sults obtained on beam-plasma experiments.In 1967, Hopman et al. published work on the

deceleration of an electron beam during the elec-tron plasma frequency instability. The interferencepattern found along the system axis presented ashrinkage of the wave length due to the decelera-tion of the beam by the unstable wave[3]. In thesame year, Vermeer et al. studied the excitation ofion oscillations as a result of the beam-plasma inter-action. They found that the interaction is excitedby the slow cyclotron wave on the beam[4].

Later, in 1968, Hopman and Ott studied the sat-uration of the beam-plasma instability, caused bya flattening of the beam distribution function[5].Clear differences were found in the beam distribu-tion function and correlated to pulse status[5]. Hop-man et al. also published a paper on the electron cy-clotron instability, regarding its characterization[6].For a limited parameter range they were ableto compare the experimental results with thetheory[6].

Then, in 1972, Wakeren and Hopman studied thetrapping of electrons as a result of the beam-plasmainteraction[7]. The entrapment is attributed to the

large amplitude of electrostatic waves that arisefrom the interaction[7].

Cabral and Varandas published a paper on thesuppression of the electron cyclotron instability in1980[1]. This suppression is attained by the injec-tion of a secondary parallel electron beam which,when in resonance, results in cyclotron dampingand causes the reduction of the cyclotron wavepower[1]. The authors also mention the importanceof this suppression mechanism for controlled fusionmachines, due to the similar behaviour between en-ergetic electron beams and the cyclotron radiationin Tokamaks, caused by runaway electrons. Therelation between cyclotron radiation and runawayelectrons was suggested by Spong et al. in 1974.

Two years later, Silva and Cabral publishedon the ion oscillations at low pressure regimes[8].These oscillations propagate in azimuthal directioninside the plasma column and were found to be ex-ited due to convection effects associated with a ro-tation of the column.

The Beam-Plasma InteractionExperiment

The apparatus is centered on a cylindricalsteel chamber with seven observation hatches,64.0±0.1cm long and 4.1±0.1cm inner radius.There, a low pressure helium gas interacts with alow energy electron beam, creating a low temper-ature plasma. The chamber is equipped with twoLangmuir probes: one fixed probe and one mov-able probe. The fixed probe is placed vertically andfixed to the chamber wall. The fixed probe posi-tioner allows to adjust the penetration depth intothe plasma column. On the other hand, the mov-able probe has fixed penetration depth but can bemoved across the length of the interaction chamber.The holder of this probe slides on two horizontalrails, allowing to perform measurements in differentpositions. The injection of gas is also made near theleft side of this section through an injection nozzle.

Globally, the structure can be divided into fivefundamental sections, connected in chain but elec-trically isolated through Bakelite rings and rub-ber seals. On the left, according to the presentedschematic, is the electron gun that generates theelectron beam. During operation this section isat an electric potential of -2kV and for this rea-son it is isolated from the remaining structure ofthe experiment. It can be divided into two parts:the inner filament holder and the shielded cylindri-cal cup where it is inserted. Between the electrongun and the interaction chamber lies the electro-magnetic resonant cavity, placed inside a cylindricalsteel section with the same radius as the interactionchamber but only 21±0.1 cm long. On the right

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Figure 1: Cross section schematic of the apparatus. Based on reference[1].

of the interaction chamber lie two sections. Thefirst holds the pulley system of the movable probecables and the vacuum measurement gauge whilethe second on the far right end, contains the elec-trostatic energy collector and the turbo-molecularvacuum pump. Additionally, the latter is directlyattached to the apparatus steel support frame. Aset of ten coils, equally displaced and aligned, sur-round the hole interaction path in order to createan homogeneous[1] magnetic field. Alongside, thereis a quadrupole visible on Figure 1 which allows tocorrect any misalignment between beam and inter-action chamber. The described parts are connectedtogether and stand on a steel bed composed by tworails bolted to the holding structure frame.

The CODACThe CODAC system implemented during the

upgrade process can be divided into three majorunits: the local-host, the control and the acquisi-tion boards. The system was designed under thescope that both boards can work and communicateseparately with the host (Figure 2). The systemwas integrated into a 3U 19-inch rack.

Figure 2: CODAC integration schematic. Bothboards can work and communicate separately withthe local-host via RS232 communication protocol.

The local-host is based on a MSI MS-9832 ITXmotherboard, with a SanDisk 60GB SDD disk, 2GB

DDR2 RAM and a 250W ATX power supply. Itruns the CentOS 6.5-x386 Linux operative systemand constitutes the central unit of the CODAC.This motherboard provides a compact solution forhosting the system with all the necessary interfaces.The serial ports allow to establish serial commu-nication with the two boards via RS232 protocol.Moreover, the Ethernet port enables to make theCODAC available through the network. This meansthat the apparatus can be operated either locally,using the host as a standalone desktop computer, orthrough the internet. All the usual desktop connec-tions are made available through the front frameshield of the local-host. The ATX power supplyis also used to supply both control and acquisitionboards and consequently all actuators and sensors.The rotating key switch is used to turn on the powersupply. The boards can be independently turned onor off via the three toggle switches present of thefront shield. Thus, starting the local-host does notimply the start of the boards.

Each board has a specific set of assigned functionsand responds directly to the host. In this appara-tus, the control board performs the following tasks:pressure measurement, control of gas injection andvalves, vacuum pumps, movable probe positioning,electron gun coolant flow and power relay board. Italready has control I/Os for the future implemen-tation of DC-DC converters for confinement coilsand filament. The power relay board is used forboth rotary and turbo pumps, water pump, vac-uum cut valve, high voltage and current power sup-plies. On the other hand, the acquisition board isoriented to acquire the signals related to the ap-paratus diagnostics: Resonant cavity transmitted,reflected and incident signals, interferometry mixedsignal and electrostatic collector signal. Besides, italso has a control line for a secondary relay boardto power on/of the RF and diagnostic equipments.

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The block diagrams for each board are presented inFigure 3.

Both control and acquisition boards are basedon dsPICnode V3.0 development boards with Mi-crochip dsPIC30F4011 and dsPIC30F4013 micro-controllers, respectively. For each board it was de-veloped an EUROCARD expansion shield, 100mmwide and 130mm long, containing the specific con-trol and acquisition electronics . The connectionbetween dsPICnode and shield is made through aDIN96 connector and the power supply via MOLEXconnectors located at the shields back panel. Withexception of the fiber optic connectors, all the backpanel connections are made with RJ45 connectors.Although both microcontroller models share manysimilar features, the reason for using different mi-crocontrollers for control and acquisition is justifiedbased on their specific characteristics. For instance,the 30F4011 has the Quadrature Encoder module,useful to interface with the movable probe positionencoder. On the other hand, the 30F4013 has 12bit-ADC resolution instead of the 30F4011 10bit-ADC,becoming a more suitable choice for the acquisitionboard. Both microcontrollers work at 30MIPS, us-ing the UART2 to establish serial communication(RS232 driver) with the host at 115200 bit/s. Inthe attachments it is possible to observe the elec-tric schematics of the dsPICnode V3.0 as well asthe shields developed during the upgrade process.

Figure 3: Bock diagrams for the control and acqui-sition boards of the CODAC system.

The communication protocol implemented in thecontrol and acquisition boards was based on thee-lab ReC Generic Diver[9]. This means that theboards are compliant with the e-lab middleware,making it possible to further integrate this appa-ratus into the e-lab platform. The high level imple-mentation into the platform was not part of this up-grade process. Nevertheless, it was possible to cor-rectly operate the apparatus using the driver spe-cific commands and state machine. Moreover, bydoing so it has been proven that it is possible to in-tegrate the Beam-Plasma with the e-lab mainframeinstalled on the local host of the CODAC.

e-Lab works under the scope of pre-configurableexperiments. It means that the user configures theapparatus for a given experimental protocol and theCODAC executes the experiment autonomously.Due to the high complexity of the apparatus, thistopic was taken under serious consideration. In or-der to provide the maximum flexibility during op-eration, several protocols are implemented for thesame diagnostic technique. For the specific caseof the interferometry, the user can start to cali-brate the alignment position between probes, thensend the probe to the power calibration positionand finally sweep the preset range of the interactionchamber with the movable probe. These operationsare performed autonomously by the microcontrollerbut their execution is dependent on the user config-uration and start command. Another feature is thatmachine parameters can be preserved between pro-tocols i.e. rotary vacuum pump keeps working dur-ing interferometry protocol changes. There is a spe-cific protocol (protocol 0) to actuate over the funda-mental apparatus parameters such as gas pressure,vacuum pumps or power relays. This implementa-tion method aims to preserve operation flexibilityand at the same time ensure compatibility with thee-lab frame work.

RF Equipment and Diagnostics

During the upgrade process, two major diagnostictechniques were rehabilitated: resonant cavity andinterferometry. These techniques depend on sensi-tive RF equipments such as generators and crystaldetectors. One of the major features of this CO-DAC project is the possibility to acquire signals andoperate both diagnostics simultaneously, improv-ing the capability to compare experimental results.Since all the original RF equipment was in perfectworking condition, all the diagnostics were imple-mented according to the original specifications.

For the resonant cavity (Figure 4) a HP 8620Asweep oscillator with 8621B RF section, a HP 777Ddual directional coupler with two HP 420A crystaldetectors, a HP 423A crystal detector and a GRC874-D20L stub were used.

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Figure 4: Schematic of connections made in order toimplement the resonant cavity diagnostic technique.

The HP 8620A sweep oscillator and 8621B RFsection provide a frequency range comprised be-tween 1.8 and 4.2GHz making it suitable to coverthe 3.6GHz resonance frequency of the cavity inTM010 mode. Besides providing fine tuning of thecentral frequency, the generator also allows to set afrequency window that can be automatically seepedin a preset time base. The generator gives an out-put DC signal comprised between 0 and 10.2V, pro-portional to frequency output into the sweep range.Thus, by knowing the frequency windows range, itbecomes possible to determine the frequency out-put of the oscillator at a given time. The 8621BRF section provides the ALC mode which was usedto flatten and control the output power level. Theoutput power was set to 4/6 of the scale with ALCINT mode on. The power was determined with theBoonton 42A Microwattmeter as oscillating around1±0.1mW. The output signal of the sweep generatorwas connected to the HP 777D dual directional cou-pler. This device allows to sample at -19.9 dB thesignal traveling from the generator to the cavity andvice-versa. Since the working range is comprised be-tween 1.9 and 4.0GHz, it allows to sample both in-cident and reflected waves at the working frequencyof the cavity. Moreover, the sampling outputs areconnected to two HP 420A crystal detectors. Theseprovide a DC signal output and consequently allowto measure the RF power for a given frequency. Be-tween the dual-coupler output and the input of thecavity, a GRC 874-D20L stub was introduced. Thisaimed to match the impedance of the load, antennaand cable, to the output of the dual-directional cou-pler. It was observed that after tuning the stubproperly (length of 10.5±0.5cm), the power deliv-ered to the load was maximized. In order to pickthe output signal of the cavity a HP 423A crys-tal detector is employed. An attempt to introducea second GRC 874-D20L stub into this path wasmade but no significant advantages were observed.Moreover, it as observed that the signal would beless intense. It was tested in the position of the firststub and it was concluded that the second stub wasnot working properly causing high insertion losses.

For the interferometry technique (Figure 5) a HP3200B VHF oscillator, a 50Ω T-junction, two VHFattenuators, one RF mixer and two VHF amplifiers

were used. The VHF generator allows to manuallytune the output frequency from 10MHz to a maxi-mum of 500MHz. This is adequate for the techniquesince the frequency range used is comprised between50 and 250MHz. The signal output connector in theback of the device also allows to regulate the powerlevel via a piston-type attenuator. The output sig-nal is divided using the T-junction, connecting oneoutput to the attenuators and the other to the fixedLangmuir probe. Both fixed and movable Langmuirprobes are used as antennas.

Figure 5: Schematic of connections made in order toimplement the interferometry diagnostic technique.

The signal injected into the plasma column ispicked by the movable probe. Due to the low signalstrength, two HP 8447A RF amplifiers were con-nected in series to provide a total gain of 40dBso the signal power would became in the order ofhundreds of micro Watt. These provide a workingrange comprised between DC and 400MHz. Finally,the HP 10514A mixer was used to mix the signalpicked by the movable probe with the one injectedinto the plasma. Since the two signals must havepower intensities as equal as possible, the signalfrom the generator must be attenuated. This wasdone through two variable attenuators connectedin series, the first scaled in steps of 10dB (HP355DVHF Attenuator, 0-120dB) and the second in stepsof 1dB (HP355C VHF Attenuator, 0-12dB). Thepower of the signals entering the mixer must neverexceed the limit of 5mW or the device will becomepermanently damaged. As the phase variations in-duced by the propagation along the cables and theRF equipment are constant, the mixing of the twosignals allows to determine the phase shift inducedby the plasma. The movable probe signal was con-nected to the R input of the mixer while the attenu-ated signal was connected to the L input. The out-put was then connected to the CODAC. It is criticalto adjust the attenuation each time the frequencyof the generator is changed during the execution ofthe interferometry technique. Moreover, the powercalibration must not be done with the two probesaligned. Tests have demonstrated that the mostsuitable position is 7±0.2mm off alignment to theleft of the fixed probe.

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Experimental Results and Dis-cussion

The most representative results for both tech-niques are addressed separately, followed by a finaldiscussion regarding both techniques.

Resonant CavityIn order to perform the resonant cavity technique,

the sweep generator central frequency was tuned forthe resonance frequency 3.588GHz. This was donewith the apparatus in high vacuum, thus with noelectron beam or gas injection. Then, a sweep win-dow of 40±2MHz was set for the oscillator to sweeparound the central frequency. The power was set to1±0.1mW with the generator ALC mode activated.

Figure 6: Resonant cavity in vacuum at2.1×10−5mbar: transmitted, reflected and incidentsignal.

Figure 6 presents the intensity of the transmitted,reflected and incident signals, under the previousexperimental conditions. It is possible to observe atransmission maximum peak centered in the reso-nance frequency, coincident with a minimum in thereflected signal. This is according to what was ex-pected since for a resonant cavity, a minimum in thereflected signal at the cavity input port correspondsto a maximum in the transmission across the cav-ity, detected in the output port. Looking in detailat both signals, it can be noticed that they are notperfectly symmetrical around the central frequencyas it could be ideally expected. The reason for thisdeformation is justified mainly by the variations inthe oscillator output power, thus in the intensityof the cavity incident signal. For instance, for fre-quencies above 30MHz, the power drop in incidentsignal causes a clear drop in both transmitted andreflected signals. To obtain the expected symme-try, the output power of the generator should be asconstant as possible. Several attempts to achievea flat power output were made but with no signif-icant improvements on the results. Nevertheless,these results allow the determination of the centralfrequency (f0) as well as the width (W) of the peak.

These values, determined without plasma and withthe cavity in high vacuum, were used as reference todetermine the frequency shift induced by the pres-ence of the column of plasma in the center of thecavity.

Figure 7: Resonant cavity transmitted signal forvacuum (2.1±0.1×10−5mbar) and for different gaspressures with an electron current of 18mA and con-finement field of 10.8±0.5mT (4±0.2A).

The current of the electron beam was set to18±0.5mA with a confinement field of 10.8±0.5mT,thus 4±0.2A in the coils, and the helium pressurewas varied from 0.01 to 0.05mbar. During this ex-perimental process, the configuration of the sweeposcillator and stub were not changed. The attainedtransmission peaks for these conditions are presenton figure 7, including the reference peak. The peakswere fitted (Lorentz) and the determined values arepresented on table 1. The table also contains thefrequency shifts between peaks and reference (∆f)and the calculated electron densities (ne). Electrondensity was calculated using expression:

(1)

ne[cm-3]

=

(8π2meε0

e2R2

a2J21 (x01)

J20 (x01a/R) + J2

1 (x01a/R)

× f0 [MHz] 106)

∆f [MHz] .

The values derived for the electron density are inthe order of 109cm−3 as expected[10]. It is also ob-servable that maintaining the remaining parametersconstant, an increase in pressure corresponds to anincrease in plasma density. The correlation betweenpressure and plasma density can be observed in Fig-ure 8. Linear correlation can be observed for pres-sure values above 0.01mbar. On the other hand,the pressure magnitude at which the experimentwas conducted is two orders of magnitude above ex-pected, 10−2mbar instead of 10−4mbar[10, 1]. Thisdiscrepancy in pressure values is addressed ahead.

The quality factor of the cavity in vacuumwas determined as the ratio between the reso-nance frequency and the peak half height width:

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Table 1: Peak Fit results for Figure 7. Electron beam current of 18±0.5mA and confinement field of10.8±0.5mT (4A).

p (mbar) f0 (MHz) W (MHz) ∆f (MHz) ne (cm−3) Q2.1±0.1×10−5 18.831±0.004 3.22±0.01 — — 11141.0±0.1×10−2 18.906±0.004 3.22±0.01 0.075±0.008 7.6±0.8×107 11142.0±0.1×10−2 20.443±0.004 3.21±0.01 1.612±0.008 1.6±0.8×109 11183.0±0.1×10−2 22.072±0.005 3.19±0.01 3.241±0.009 3.3±0.9×109 11264.0±0.1×10−2 23.566±0.005 3.14±0.01 4.735±0.009 4.8±0.9×109 11445.0±0.1×10−2 25.753±0.005 3.12±0.02 6.922±0.009 7.0±0.9×109 1152

Figure 8: Correlation plot between pressure andelectron density determined with the resonant cav-ity technique.

Q=f0/W0=1114. Theoretically, the quality factorof the resonant cavity is approximately 17900 fora surface resistance RS of 15.63mΩ[10]. The dif-ference can be justified based on the fact that thetheoretical formula assumes a cavity without losses,which cause broadening of the resonance peak, re-sulting in a reduction on the quality factor[10]. Thetwo holes is the cavity tops also cause a reduction inthe quality factor in 5.6%[10], due to the formationof fringing fields[11]. In the apparatus, the cavityis not isolated but instead integrated into a morecomplex system such as in a wave guide - cavity intransmission. The connections between the waveg-uide elements - interaction chamber, electron gunsection, loop antennas - create load for the cavityand consequently induce a drop in the quality factor(quality factor under load)[11, 10]. Also, the con-nection between the cooper cylinder and the topscreates additional Joule losses.

Nevertheless, the expected value for the exper-imental quality factor should be approximately2000[10], thus in the same order of magnitude of thedetermined value. Moreover, it can be also observedthat the quality factor increases with the increasein electron density. This is also as expected due tothe fact that the central part of the cavity was filledwith a plasma column, thus with ε < ε0[10].

Interferometry

To perform the interferometry diagnostic tech-nique, several configurations of confinement fieldand electron beam current were tested. For a con-finement field of 10.8±0.5mT, the threshold beamcurrent was found to lie between 10 and 12mA forpressures in the order of 10−2mbar. The lowerlimit pressure was of 1.0±0.1×10−2mbar. The pres-sure range should be 10−4mbar[10], thus two or-ders below. At this pressure, no conclusive resultswere found and the experiment was conducted un-der the previous conditions. The most expressiveresults here represented were attained for a pres-sure of 3.0±0.1×10−2mbar, electron beam currentof 18±0.5mA and confinement field of 10.8±0.5mT(4A).

Figure 9: Plasma E(x) patterns for three specificfrequencies in the sweeped range.

In this technique, the wave number k is deter-mined by imposing fixed values of frequency to thesystem. The frequency was varied between 70 and200MHz and the E(x) patterns were registered us-ing the CODAC (Figure 9). For each measurement,the power level of the signals entering the mixerwas calibrated using the microwattmeter and at-tenuators. The wavelengths were determined tothe left and to the right side of the fixed probeby measuring the distance between points with thesame phase. For frequencies above 190MHz, it wasobserved that the E(x) pattern did not exhibitedany measurable wavelengths. This is due to thefact that the frequency imposed by the VHF os-cillator is close to the plasma frequency, thus in

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the limit where wave propagation passes from realto evanescent[10]. Moreover, it was also observedthat as the imposed frequency increases, the wave-length decreases until no phase variation is observedand evanescent propagation is established (ampli-tude variation[10]). The difficulty in determiningfpe by changing the imposed frequency results fromthe presence of the electron beam which affects theplasma dispersion diagram[10]. The presence of theelectron beam was disregarded in this analysis butit was still possible to conclude that the plasma fre-quency should lie between 200 and 220MHz. Forfrequencies bellow 70MHz the wavelength is largerthat the sweep range of the movable probe makingit impossible to perform any usable measurements.

Figure 10: Plasma dispersion relation for an elec-tron beam current of 18mA.

The most adequate method for determining theplasma frequency consists on fitting the pairs (f,k)with the expression for the dispersion relation, thusreconstruct the diagram for dispersion relation ofthe plasma for frequencies below fpe. This was donefor values determined to the left (superscript -) andto the right side (superscript +) of the fixed probe,separately. By considering the cyclotron frequencyto be 302±14MHz, it was possible to retrieve theplasma frequency and the transverse wave numberp for both situations. These results are displayed onTable 2, along with the calculated plasma densityand plasma column radius a=2.405/p.

On the last column of Table 2 are presented theaveraged values of the parameter p calculated withthe (f,k) pairs, using the plasma dispersion rela-tion and the empirical value of plasma frequency(200MHz). It is possible to observe that the valuesfrom both methods are in the same order of mag-nitude, with differences covered by the errors. Theradius of the plasma column in also in the expectedorder of magnitude, corroborating the hypothesisthat the interaction chamber is not completely filledwith the plasma column - partially filled cylindricalwaveguide. During the experimental trial it was dif-ficult to visually determine the actual radius of theplasma column. Nevertheless, this value was esti-mated in approximately two centimeters, thus com-parable with those from the dispersion equation fit.

Moreover, it was also observed that the visible ra-dius of the plasma column was not constant alongthe plasma column. This was attributed to the factthat the confinement field not being completely ho-mogeneous across the full length of the interactionchamber.

Looking at the results displayed on Table 2, itis possible to observe that the plasma frequencydetermined to the left of the fixed probe is largerthan to the right. These results are critical sincethey corroborate the hypothesis that the densityof the plasma decreases along the plasma column,thus along the interaction path of the electron beamwith the low pressure helium gas[10]. Moreover, theplasma order of magnitude for the plasma densityis within the expected range of 108cm−3.

It should be also noticed that for frequencies closeto the plasma frequency, small variations on thedensity induce large variations on k due to the lowgroup velocity at this frequency range[10]. Thisphenomena may justify the discrepancy found be-tween the plasma frequency from the fits and theexpected value. Although the plasma frequency re-trieved from the fits was coincident with the em-pirical limit of 200MHz, the difference between theactual plasma frequency and this limit was expectedto be higher.

Overall Assessment

Comparing the density results obtained by bothtechniques (Table 3) for the same experimental con-ditions, it is possible to observe that the densityof the plasma decreased along the plasma column,from the electron gun to the electrostatic collector.The plasma is generated by the interaction betweenthe low density gas and the electron beam, thus itcan be expected that the density of the plasma de-creases along the interaction path.

Table 3: Comparison between density results de-termined with resonant cavity and interferome-try techniques under the same experimental con-ditions: pressure of 3.0±0.1×10−2mbar, electronbeam current of 18±0.5mA and confinement fieldof 10.8±0.5mT.

Resonant Cavity Interferometry3.3±0.9×109cm−3 5.0±0.1×108cm−3

Nevertheless, the density values differ in one or-der of magnitude and the respective errors do notcover the difference between values. This can beexplained based on two main reasons.

In Expression 1, used to determine the densityvia the resonant cavity diagnostic technique, it wasassumed that the diameter of the plasma columninside the cavity (a) was equal to the diameter of

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Table 2: Fit results for plasma dispersion relation from Figure 10, calculated parameters and comparisonwith average transverse wave number p averaged from the (f,k) pairs. Electron beam current of 18±0.5mA.

k(f) Fit Calculated Parameters p(f)fpe (MHz) p (cm−1) a (mm) ne (cm−3) p (cm−1)

k− (left) 202±4 0.90±0.05 27±1 5.1±0.2×108 0.9±0.6k (average) 200±1 0.91±0.03 26.4±0.9 4.96±0.05×108 0.9±0.5k+ (right) 194±2 0.84±0.04 29±1 4.7±0.1×108 0.9±0.5

the cavity passing holes. Actually, the plasma col-umn created inside the cavity by the electron beamand helium gas interaction is not confined to thesize of the holes. Instead, the plasma diffuses in-side the cavity, presenting a radius larger than theone considered initially[12] (Figure 11). The previ-ous assumption is a reasonable initial approxima-tion since it is not possible to know in advance theradius of the plasma column. The actual value ofthe plasma column radius (a’ ) can be estimated byconsidering the density determined by the interfer-ometry technique, the measured frequency shift inthe cavity under the same conditions and the innerradius of the cavity (R). These values were used tonumerically solve Expression (1) which returned aplasma column radius a’ of 14.7mm, approximatelyhalf of R as it could be expected[12]. It can also beobserved that a’ is approximately three times thevalue considered in the first approximation. Giventhese considerations, the actual value for the radiusmust be lower than 14.7mm but significantly higherthan 5mm. This correction would lead to cavitydensity values larger than in the interferometry butyet in the same order of magnitude.

Figure 11: Plasma column inside the cylindrical res-onant cavity where a is the radius of the passingholes and a’ is the actual radius of column.

The discrepancy can also be explained based onthe existence of a pressure gradient inside the ap-paratus caused by the vacuum pump. If the heliumpressure decreases along the interaction path so willthe density of the plasma leading to the observed re-sults. The same mechanism can be used to explainthe absence of plasma at pressures of 10−4mbar aswell as the first ionization of the helium gas. In

order to achieve lower pressures, it is necessary toresort to the turbo-molecular pump. The pump willlargely increase the pressure gradient inside the in-teraction chamber, making it difficult to create theplasma.

The results published regarding thisapparatus[10, 1] revealed a different config-uration which may partially corroborate theprevious discrepancies. The right end section ofthe apparatus where the turbo-molecular pump ispresently connected was longer, providing a largerinner volume between the pumps and the inter-action chamber. This extra volume could largelydecrease the formation of a significant pressuregradient along the interaction path. Moreover,the turbo-molecular pump, which replaced theoil diffusion pumps, was designed for a volume of150L whereas the inner volume of the apparatusis approximately 15L. Furthermore, under theprevious configuration, the vacuum gauge waslocated directly above the diffusion pumps whichmay have induced pressure readings below theactual pressure inside the interaction chamber.Based on these assumptions, it can be concludedthat the pressure gradient formation is a criticalmatter to the operation of the apparatus and mustbe addressed in the future. Another fundamentalissue is to study plasma formation for pressuresof 10−3mbar. At lower pressures, no plasma wasdetected and for higher pressures the helium gaswas clearly in the second ionization regime. Sincethe best regime for performing experiments in thisapparatus is the first ionization of the helium[10],it is critical to find under which specific conditionsthis regime appears.

The implementation of the CODAC system in theBeam-Plasma experiment has successfully allowedthe rehabilitation of the resonant cavity and inter-ferometry diagnostic techniques. Moreover, the ex-perimental protocols to study the plasma param-eters can now be implemented systematically andwithin conditions of reproducibility. Additionally,the experimental results have shown that the ap-paratus is working with the expected performanceand it can now be used to perform advanced exper-imental works on plasma physics.

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Conclusions and Future Work

The main goal of the present project was to re-habilitate and upgrade the Beam-Plasma appara-tus in order to make it compliant with the mostrecent solutions for control and data acquisition soit could be used for advanced experimental workson plasma physics. This constituted a significantchallenge since the original integrity of the set-upshould be preserved. The upgrade conducted onthe set-up allowed to understand and document themechanisms and techniques used in its construc-tion. Moreover, it provided the necessary insightto correctly integrate both sensors and actuators,thus to guarantee that the CODAC would becomeintegral part of the apparatus. The CODAC wasdesigned to allow future expansions and modifica-tions but at the same time making the control andacquisition hardware compliant with the e-lab plat-form. Experimental trials conducted on the appara-tus showed that both interferometry and resonantcavity diagnostic techniques are working properlyand can be used to determine fundamental plasmaparameters. Also, it became possible to gain insightover the physical mechanisms behind the techniquesand consequently on how the different apparatusparameters affect the plasma.

Despite being operational, the process of com-pletely upgrading this apparatus is not yet con-cluded. It is still necessary to develop power sup-plies for the electron gun filament, confinement coilsand quadrupole that can be integrated into theCODAC. Moreover, it could be interesting to fullyautomate the radio frequency equipments in orderto make them accessible through the CODAC. Al-though it was possible to show that the apparatuscan actually be integrated into the e-lab platform,no GUI was developed at this stage. Equipping theCODAC with this feature would be a considerableimprovement to its usability. An interesting alter-native for e-lab integration would be to have oneof the CODAC boards directly connected to the e-lab hardware server while the other is connectedthrough the first one. This configuration requiresonly one serial communication port at the hard-ware server for the hole CODAC system and, atthe same time, preserves all the available features.The gas pressure PID implementation still requiresoptimization in order to reduce the set-point set-tling time. Finally, reducing the pressure gradientinside the apparatus is critical to conduct exper-iments at lower pressures, which can possibly beachieved by throttling the connection between theturbo-pump and the apparatus. These future im-provements would certainly extend the experimen-tal scope of the apparatus, giving continuity to thepresent upgrade work.

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