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The change in magnetic energy and magnetic helicity has been measured during the sawtooth relaxation in the Madison Symmetric Torus reversed-field pinch. The larger decay of the energy (4.0%- 10.5%), relative to helicity decay (1.3% - 5.1%), modestly supports the helicity conservation hypothesis in Taylor's relaxation theory. However, the observed helicity change is larger than the simple magnetohydrodynamics prediction. Enhanced fluctuation-induced helicity transport during the relaxation is observed. PACS numbers: 52.30.Jb, 52.25.Gj, 52.55.Hc Magnetic helicity (1) is a measure of the "knottedness" of magnetic field. It is an invariant within a flux tube in a perfectly conducting plasma. In 1974 Taylor conjectured (2) that in a "slightly" resistive plasma the total helicity is well conserved during plasma relaxation in which the magnetic energy decays toward a minimum-energy state. This well-known hypothesis has been successful (2) in explaining magnetic structures in laboratory plasmas, such as the reversed-field-pinch (RFP), spheromak, and multipinch. It has also been applied to relaxation in tokamak (3,4), magnetospheric (5), and solar (6) plasmas. The conjecture has been extended theoretically (7) and studied through nonlinear MHD computations (8 -11). However, to our knowledge, this rather well-accepted conjecture has received little experimental test. Helicity conservation has been inferred by applying the helicity balance equation to a spheromak (12) and in the RFP (13). In this Letter, we report an experimental investiga- tion of the magnetic helicity and energy evolution dur- ing plasma relaxation in the Madison Symmetric Torus (MST) RFP. The test of Taylor's conjecture is possi- ble since relaxation occurs in the MST as events which are discrete in time (corresponding to the 100 ms crash phase of a sawtooth oscillation). We find that during the relaxation event the magnetic helicity decreases by 1.3 - 5.1 %, while the magnetic energy decreases by 4.0- 10.5 %. (Smaller helicity decay corresponds to smaller energy decay.) Hence the helicity conservation conjec- ture is modestly well satisfied in that the helicity decay is less than the energy decay by a factor of 2 -3. Interest- ingly, the relatively violent sawtooth crash only dissipates a small fraction of the magnetic energy (presumably con- strained by the relative conservation of helicity). How- ever, the helicity decay is greater than that expected from simple resistive MHD arguments. The gauge-invariant definition of the total helicity in a toroidal plasma is given by (14) K ; R A ? B dV 2 FfsadFusad where A is the vector potential, B is the magnetic field, Ffsad is the total toroidal flux, Fusad is the poloidal flux threading the central hole of the torus, and the integration is over the plasma volume. Taylor evaluated (2) a relaxed state by minimizing the magnetic energy W › R sB2y2m0ddV , subject to the constraint of constant helicity. The resulting field satisfies the equation = = =3 B › l B , where the current to field ratio l ; m0j ? ByB2 is a spatial constant. The Bessel function solutions to this equation (referred to as the Bessel function model, BFM) approximate well the measured fields in the RFP, except that in experiments l falls to zero at the edge. The MST (15) is a large RFP device (R › 1.50 m, a › 0.52 m) with plasma current Ip up to 700 kA. The plasma is surrounded by a 5-cm-thick aluminum shell with one toroidal and one poloidal gap. The shell also acts as the vacuum vessel and a single-turn toroidal field coil. Magnetic energy and helicity enter through the gaps across which nonzero toroidal Vfsad and poloidal Vusad voltages occur. Sawtooth oscillations (16) in the MST consist of a fast crash phase and a slow recovery phase. The plasma rapidly relaxes towards its minimum energy state during the crash within 0.2 ms. This is illustrated by changes in two dimensionless parameters: the reversal

Conservation of Magnetic Helicity during Plasma Relaxation