MODELOS DE SERIES DE TIEMPO: MEDIA Y VARIAN-

As previously discussed, RF ground loop is unavoidable in high-speed diagnostics. However, it is possible to reduce or even eliminate the impact from the RF ground loop. Perkins & Bellan 2011 [89] identified a large RF ground loop as the cause of radio frequency noise in a vacuum extreme ultraviolet probe array and invented a RF ground current diverting technique to prevent the RF ground current from interfering with measurement.

Figure 5.5 illustrates the principles of this RF ground current diverting technique. A capacitive coupling exists between a grounded conducting surface (e.g., chamber wall) and the outer conductor of the coaxial cable of a probe. This allows an RF ground current to flow on the outer conductor of the coax cable. A high frequency ferrite core is placed around the coaxial cable next to the data acquisition device. A short wire (low impedance

Ferrite

data 

acquisition

Bypass

10 cm

To probe

Coax cable

Figure 5.5: RF Ground loop diverting technique invented by Perkins & Bellan 2011 in [89].

shunt) links the ground of the data acquisition device to the outer conductor of the coax cable before the ferrite core.

The effective schematic diagrams of the configuration are plotted in Fig. 5.6. Consider a high frequency current caused by an RF ground loop. This current flows on the outer conductor of the coaxial cable and generates magnetic field around the cable. Because the ferrite has large magnetic permeability, the surface current experiences a large inductance due to the ferrite core. At high frequency large inductance gives large impedance. On the other hand, because a grounded bypass (shunt) with lower impedance is provided before the ferrite core, the surface current will be diverted to ground before the data acquisition device (Fig. 5.6B). Therefore the RF ground current does not impact the data acquisition device. The signal current, on the other hand, is equal and opposite on both the inner and outer conductor of the coaxial cable. The signal current does not generate any magnetic field outside the coaxial cable and so does not experience the external ferrite core.

The RF ground current diverting is an intelligent way to reduce the impact of RF ground loop. It is only effective to the surface current induced by the RF ground loop and has no effect on the signal being measured.

Center conductor

Outer conductor

Ferrite

50 Ωdata  acquisition High freq RF surface current

Center conductor

Outer conductor _Ferrite

50 Ωdata  acquisition signal current

A

B

Figure 5.6: Effective schematics of the RF Ground loop diverting technique for signal current (panel A) and RF ground loop current (panel B).

We built a dummy probe to study the RF ground loop. A dummy probe is a probe that in theory should output absolute zero signal. Figure 5.4 shows a sketch of dummy probe in the right panel. The dummy probe is made of a single 1 m long 0.047 in semi-rigid coax cable. One end of the coax cable is the 6 mm diameter probe and the other end is mounted with a female SMA connector. Unlike the loop probe, the dummy probe does not have the gap between the outer conductor. Therefore the B-dot loop formed by the inner conductor is fully covered by the outer conductor. When the dummy probe is in a time-dependent magnetic field, an eddy current can be induced in the outer conductor loop. The thickness of the outer conductor of the semi-rigid coax cable is 0.125 mm, equal to the skin depth of copper at f = 250 KHz. Therefore magnetic fluctuation above 1 MHz is not able to diffuse through the outer conductor and be picked up by the dummy probe.

We tested the dummy probe in four different configurations to identify and solve the RF ground loop problem.

Configuration 1: flexible coax cable In this configuration, we used a 8 m long RG58 50 Ω flexible coaxial cable to connect the probe and the data acquisition device. Figure5.7 gives the 2 MHz high-pass filtered signal from the dummy probe and the corresponding

5 10 15 20 25 30 35 −0.01 −0.005 0 0.005 0.01 time (µs) output (V)

dummy probe signal (>2 MHz)

0 5 10 15 20 25 30 0 0.2 0.4 0.6 0.8 1x 10 −3 Freq (MHz) spectra (V) Fourier Transform shot# 16876 5 10 15 20 25 30 35 −0.01 −0.005 0 0.005 0.01 time (µs) output (V)

dummy probe signal (>2 MHz)

0 5 10 15 20 25 30 0 1 2 x 10−4 Freq (MHz) spectra (V) Fourier Transform shot# 16883 5 10 15 20 25 30 35 −0.01 −0.005 0 0.005 0.01 time (µs) output (V)

dummy probe signal (>2 MHz)

0 5 10 15 20 25 30 0 1 2 x 10−4 Freq (MHz) spectra (V) Fourier Transform shot# 16884 5 10 15 20 25 30 35 −0.01 −0.005 0 0.005 0.01 time (µs) output (V)

dummy probe signal (>2 MHz)

0 5 10 15 20 25 30 0 1 2x 10 −4 Freq (MHz) spectra (V) Fourier Transform shot# 16892

Figure 5.7: Output signals (left panels) of the dummy probe in different configurations and the corresponding power spectra (right panels). From top to bottom: (1) shot 16876, dummy probe with flexible coax cable; (2) shot 16883, dummy probe with semi-rigid coax cable; (3) shot 16884, dummy probe with semi-rigid coax cable and RF ground loop diverting (Fig.5.5); (4) shot 16892, similar to (3) but with the semi-rigid coax cable wrapped around the ferrite core by four turns. In all four left panels, components below 2 MHz have been numerically filtered out using a 4-th order Butterworth digital filter. The y-axis of the first spectrum plot (shot 16876) is 4 times higher than other spectra plots.

spectrum (shot 16876). High frequency noises are found at 8 µs and after 17 µs, with amplitude ∼0.01 V and frequencies primarily at 5 MHz, 10 MHz, 15 MHz, and 20 MHz. Note that without any shield the electrostatic probe picked up∼1 V signals at∼8µs and after 28µs in the range of 5−15 MHz. These results suggest that there exists a RF ground loop in both the dummy probe and the electrostatic probe, with resonant frequencies at 5 MHz, 10 MHz,. . .. The actual capacitive signal by the electrostatic probe should be lower than 1V, but is amplified by the RF ground loop at the resonant frequencies.

Configuration 2: semi-rigid coax cable In this configuration, we replace the 8 m long flexible coaxial cable with a 5 m long RG402 50 Ω semi-rigid coaxial cable. The second row of Fig.5.7shows the signal and spectrum of this configuration (shot 16882). The semi-rigid coaxial cable provides a much better EMI/RFI shield to the central conductor and gives much less noisy output. However, the RF ground loop resonances still exist.

Configuration 3: semi-rigid coax cable + RF diverting In this configuration, we apply the RF ground loop diverting technique by putting a high frequency ferrite core and a short shunt cable at the end of the semi-rigid coaxial cable, as shown in Fig.5.12. The third row of Fig.5.7gives the results in this configuration (shot 16884). The high frequency MHz RF ground currents are all reduced by≈50% compared to shot 16883. These validates our conjecture that these high frequency components are caused by a RF ground loop. However, the RF ground current is not fully eliminated by the ferrite and the shunt.

Configuration 4: semi-rigid coax cable + RF diverting with four turns around the ferrite core The spectra of shot 16883 and 16884 shows that the shunt in shot 16884 diverts about 50% of the RF ground current, implying that the inductance of the shunt is comparable to the inductance caused by the ferrite core. In order to divert more RF ground current through the shunt, we wrap the semi-rigid coax cable around the ferrite core by four turns. The inductance due to the ferrite seen by the surface current is expected to be 16 times as large as before. The last row of Fig.5.7shows the dummy probe output in this configuration (shot 16892). The resonances at 5 MHz, 10 MHz, 15 MHz and 20 MHz are essentially removed. The noises at 8 µs and 30 µs are reduced to the quiescent noise level 0.0005 V. The enormous resonance at 15 MHz is reduced from 0.8×10−3 V in shot 16876

to 1.2×10−5 V in short 16892, corresponding to a 66 times reduction in noise level or 36 dB attenuation in noise power.

In this section we studied RF ground loop by testing a dummy probe in several different configurations. We show that by properly applying the RF ground current diverting tech- nique by Perkins & Bellan 2011 [89], the RF ground current can be essentially eliminated. The quiescent level of the dummy probe is 0.5 mV, comparable to the digitization error of the data acquisition device (1/212) V= 0.24 mV. Recall that without any capacitive shield- ing or RF ground current diverting, the electrostatic probe picked up ∼1−2 V signals at 8µs and after 28 µs. Therefore a ∼3000 times reduction in electrostatic signal is achieved by using the shielded loop and RF ground current diverting technique, corresponding to a 70 dB rejection of electrostatic noise.

5.3.2 Construction of the 3D magnetic probe

Six shielded loop probes are constructed. Each probe is made out of a 1.7 m long 0.047 inch diameter semi-rigid coaxial cable (part no. SR-047ST-TC, crossrf.com) with one end forming the 6 mm diameter shielded loop probe (left panel of Fig. 5.4) and the other end mounted by a female SMA connector. The loop probe is painted by a layer of high voltage insulating varnish (10-9002, red GLPT insulating varnish, GC electronics) and the long tail of the semi-rigid coax cable between the probe and the SMA connector are protected by fiberglass sleeving (Bentley-Harris, size 12).

The radius of the central connector of the semi-rigid coax cable is a= 0.144 mm. The inductance of the single loop probe is therefore Lp =µ0r ln8_ar −2

= 6.5 nH according to Eq.5.9, wherer = 3 mm is the radius of the loop. Equation5.8then shows that the probe is capable of measuring up to 1.2 GHz magnetic fluctuation. At 10 MHz, the attenuation factor of the probe due to finite self-inductance is 0.99997 and the phase delay is just 0.46◦. Two identical probes are placed next to each other but with the loops facing in opposite directions. As shown in Fig.5.8, when a changing magnetic fielddB/dtis perpendicular to both, the outputs of the two loop probes are

V1 = A dB dt +Vc V2 = −A dB dt +Vc,

V₁ V₂

dB/dt

Figure 5.8: Sketch of a pair of magnetic probes facing opposite direction.

whereA=πr2 is the cross-section area of the single shielded loop and Vcare the common

signal including capacitive coupling signal and RF ground loop current. The two probes are expected to have the same common signal because they are placed at the same location. The difference of the two probes’ outputs is

Vd≡V1−V2= 2A

dB

dt. (5.14)

The common mode is thus eliminated and only the differential mode (magnetic field mea- surement) survives. Similar techniques can be found in other high frequency magnetic diagnostics [76]. It is important to point out that for these dual differential probes, the two sub-probes need to be placed at the same location so that the capacitive coupling between the probes and the plasma are the same.

Three pairs of the dual differential probes were made and placed orthogonal to each other as illustrated in Fig.5.9. The overall size of the 3D probe is about 6 mm in diameter and 1 cm in length. In Fig. 5.10 we show the vacuum assembly of the high frequency 3D magnetic probe. The probe is enclosed in a 30 cm long, 8mm inner-diameter (ID), and 10mm outer-diameter (OD) quartz tube. The tails of the loop probes (semi-rigid coax cables) are wrapped around by insulating tape that contacts with the quartz tube firmly to prevent sliding. The quartz tube is glued to a 3/4 inch OD custom-made stainless steel (SS) cylindrical adapter by high vacuum Torr Seal epoxy. The 3/4 inch SS adapter is 1.5

r

z

θ

6 mm

10 mm

8 mm

Figure 5.9: Sketch of the three pairs of dual differential probes enclosed in a 8 mm ID quartz tube.

inch (38.1 mm) long and has an 11 mm diameter 33.1 mm deep cylindrical socket from one side and an 9 mm diameter 5 mm deep cylindrical socket from the other side. The quartz tube fits inside the 11 mm diameter socket against the 9 mm diameter socket. The 3/4 inch SS adapter is welded to a Swagelok SS-12-VCO-3 O-Ring face Seal VCO fitting. This VCO fitting has a 3/4 inch diameter tube socket that well fits the 3/4 inch SS adapter. The SS- 12-VCO-3 fitting is against to a Swagelok SS-12-VCO-1-12 VCO seal threaded connector, with an O-ring in between. The O-ring vacuum connection is secured by a Swagelok SS- 12-VCO-4 316 SS female nut that threads on the SS-12-VCO-1-12 connector. The other end of the SS-12-VCO-1-12 connector is welded to a polished 1 m long 3/4 inch OD 304 SS tube (McMaster-Carr, part no. 1750T116). The 3/4 inch SS tube is mounted through a 2.75 inch flange on the vacuum chamber by a 0.75 inch quick-connect coupling (Kurt J. Lesker, part no. F0275XVC075). Outside the vacuum chamber, the SS tube is through a custom-made 1.5 inch OD 0.75 inch ID aluminum tube attached to the 2.75 inch flange, with two lateral 1/4−20 set screws threaded in the aluminum tube to hold the central 3/4 inch SS tube.

Figure 5.11 gives the photos of two single shielded loop probes and the finished 3D magnetic probe in front of the coaxial electrodes. Figure5.12shows a photo indicating that the coaxial cables of the probe are wrapped around the ferrite cores and the short cables connect the outer conductors of the coax cables to a ground strip before the ferrite cores.

300 mm

Quartz tube 

ID=8mm OD=10mm

SS‐12‐VCO‐3 gland 

Weld point

Torr seal

O‐ring

SS‐12‐VCO‐4 nut

SS‐12‐VCO‐1‐12 

connector

¾” stainless 

steel tube

Weld point

¾” stainless 

steel adapter

Figure 5.10: Drawing of the vacuum assembly of the 3D magnetic probe. See the text description for details.

Red GLPT 

insulating varnish

Fiberglass 

Sleeving

Coax electrodes

3D magnetic 

probe

Figure 5.11: Left: photo of two single turn shielded loop with red insulating painting and fiberglass sleeving. Right: photo of the 3D magnetic probe in the vacuum chamber.

Ground metal strip

Ground wire (shunt)

Ferrite cores

to probes

Figure 5.12: Photo of the ferrite cores and shunt cables used for diverting the RF ground current flowing on the surface of semi-rigid coaxial cables of the magnetic probe.