Relative magnetic helicity is conserved by magneto-hydrodynamic evolution even in the presence of moderate resistivity. For that reason, it is often invoked as the most relevant constraint to the dynamical evolution of plasmas in complex systems, such as solar and stellar dynamos, photospheric flux emergence, solar eruptions, and relaxation processes in laboratory plasmas. However, such studies often indirectly imply that relative magnetic helicity in a given spatial domain can be algebraically split into the helicity contributions of the composing subvolumes, i.e., that it is an additive quantity. A limited number of very specific applications have shown that this is not the case. Progress in understanding the non-additivity of relative magnetic helicity requires removal of restrictive assumptions in favour of a general formalism that can be used both in theoretical investigations as well as in numerical applications. We derive the analytical gauge-invariant expression for the partition of relative magnetic helicity between contiguous finite-volumes, without any assumptions on either the shape of the volumes and interface, or the employed gauge. The non-additivity of relative magnetic helicity in finite volumes is proven in the most general, gauge-invariant formalism, and verified numerically. More restrictive assumptions are adopted to derive known specific approximations, yielding a unified view of the additivity issue. As an example, the case of a flux rope embedded in a potential field shows that the non-additivity term in the partition equation is, in general, non-negligible. The relative helicity partition formula can be applied to numerical simulations to precisely quantify the effect of non-additivity on global helicity budgets of complex physical processes.
Volume Dependence of Helicity-based Eruption Diagnostics in Recurrent Coronal Jets
School of Astronomy and Space Science and Key Laboratory of Modern Astronomy and Astrophysics, Nanjing University（南京大学天文与空间科学学院与现代天文学和天体物理学重点实验室）；National Key Laboratory of Deep Space Exploration/School of Earth and Space Sciences, University of Science and Technology of China（中国科学技术大学深空探测全国重点实验室/地球与空间科学学院）；Institute for Space-Earth Environmental Research, Nagoya University（名古屋大学宇宙地球环境研究所）；School of Earth and Space Sciences, Peking University（北京大学地球与空间科学学院）
Distribution of magnetic helicity and energy with height in solar atmosphere
State Key Laboratory of Solar Activity and Space Weather, National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台太阳活动与空间天气国家重点实验室）；University of Chinese Academy of Sciences（中国科学院大学）
Conservation of magnetic-helicity fluctuations due to spatial decorrelation of fluxes in decaying MHD turbulence
Research School of Astronomy and Astrophysics, Australian National University（澳大利亚国立大学天文与天体物理研究学院）；Australia’s Climate Simulator (ACCESS-NRI), Australian National University（澳大利亚气候模拟器（ACCESS-NRI），澳大利亚国立大学）；Princeton Center for Theoretical Science（普林斯顿理论科学中心）；Department of Applied Mathematics and Theoretical Physics, University of Cambridge（剑桥大学应用数学与理论物理系）；Gonville & Caius College（冈维尔与凯斯学院）；Canadian Institute for Theoretical Astrophysics, University of Toronto（多伦多大学加拿大理论天体物理研究所）
