Characterization of compact-toroid injection during formation, translation, and field-penetration
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 REVIEW OF SCIENTIFIC INSTRUMENTS 87, 11D409 (2016)
Enhanced magnetic field probe array for improved excluded flux calculations on the C-2U advanced beam-driven field-reversed configuration plasma experiment
T. Roche,a) M. C. Thompson, R. Mendoza, I. Allfrey, E. Garate, J. Romero, and J. Douglass
Tri Alpha Energy, P.O. Box 7010, Rancho Santa Margarita, California 92688, USA
(Presented 6 June 2016; received 3 June 2016; accepted 6 July 2016; published online 1 August 2016)
External flux conserving coils were installed onto the exterior of the C-2U [M. W. Binderbauer et al., Phys. Plasmas 22, 056110 (2015)] confinement vessel to increase the flux confinement time of the system. The 0.5 in. stainless steel vessel wall has a skin time of ⇠5 ms. The addition of the external copper coils e↵ectively increases this time to ⇠7 ms. This led to better-confined/longer-lived field-reversed configuration (FRC) plasmas. The fringing fields generated by the external coils have the side e↵ect of rendering external field measurements invalid. Such measurements were key to the previous method of excluded flux calculation [M. C. Thompson et al., Rev. Sci. Instrum. 83, 10D709 (2012)]. A new array of B-dot probes and Rogowski coils were installed to better determine the amount of flux leaked out of the system and ultimately provide a more robust measurement of plasma parameters related to pressure balance including the excluded flux radius. The B-dot probes are surface mountable chip inductors with inductance of 33 μH capable of measuring the DC magnetic field and transient field, due to resistive current decay in the wall/coils, when coupled with active integrators. The Rogowski coils measure the total change in current in each external coil (150 A/2 ms). Currents were also actively driven in the external coils. This renders the assumption of total flux conservation invalid which further complicates the analysis process. The ultimate solution to these issues and the record breaking resultant FRC lifetimes will be presented. Published by AIP Publishing. [http://dx.doi.org/10.1063/1.4960061]
    I. INTRODUCTION
The C-21 machine at Tri Alpha Energy (TAE) was upgraded in the fall of 2014 after achievement of a field- reversed configuration (FRC) with lifetime >5 ms. This upgrade resulted in C-2U, the advanced beam-driven FRC plasma experiment. Its mission was to show FRC sustainment for a period >5 ms which was accomplished in June of 2015. With sustainment times this long, plasma lifetimes were also extended to >10 ms. The primary measurement for verification of these results came from magnetic field data; in particular quantification of the excluded flux radius (r  ) of the plasma which is approximately equal to the separatrix radius (rs) of the FRC.3 The balance of pressure due to the toroidal current of the FRC, plasma energy content and the externally applied magnetic field determine the value of rs.
In Sec. II we will discuss some changes made to the C-2 vessel that were necessary to achieve our result. Then we will detail the modifications to the C-2 magnetic field probe array2 required to accurately determine r   in Sec. III. In Sec. IV we discuss the analysis procedure which takes us from raw signal to radius. And in Sec. V we present the e↵ect
Note: Contributed paper, published as part of the Proceedings of the 21st Topical Conference on High-Temperature Plasma Diagnostics, Madison, Wisconsin, USA, June 2016.
a)troche@trialphaenergy.com
of actively increasing the confining magnetic field on plasma lifetime.
II. VESSEL IMPROVEMENT
To determine r   we measure the axial component of the magnetic field (Bz(t)) just inside the wall as a function of time. The field at the wall increases due to the presence of the net-flux-free FRC and its diamagnetic nature. This would be su cient if the vessel wall was a perfect flux conserver. However, this is not the case. The vacuum vessel has a resistive decay time of ⇠5 ms. In C-2 the loss of flux due to eddy current decay was measured by additional magnetic field probes just outside the wall.2 With C-2U plasma lifetimes >10 ms, increasing the e↵ective wall time was required to maintain pressure balance. This was accomplished by wrapping 6 external flux conservers (ExFCs) along the axis of the vessel at z = ±15, ±70, and ±140 cm. They consist of 20 windings of copper wire each. They can be shorted individually or in pairs to serve as passive conservers or driven to e↵ectively add magnetic pressure to the system during a shot. The currents in these coils have the unintended consequence of distorting the signals measured by the external probes as some of them were essentially under the coils. In these cases the fringing fields produced an e↵ective magnetic field that was no longer representative of the lost flux. To fully understand the e↵ects of the coil currents we installed
 0034-6748/2016/87(11)/11D409/3/$30.00 87, 11D409-1 Published by AIP Publishing.




















































































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