Chanteur, G.: Spatial Interpolation for four spacecraft: Theory, in: Analysis methods for multi-spacecraft data, edited by: Paschmann, G. and Daly, P. W., European Space Agency Publ. Division, Noordwijk, the Netherlands, 349–370, ISBN 1608-280X, 1998.
Chanteur, G. and Harvey, C. C.: Spatial interpolation for four spacecraft: Application to magnetic gradients, in: Analysis methods for multi-spacecraft data, edited by: Paschmann, G. and Daly, P. W., European Space Agency Publications Division, Noordwijk, the Netherlands, 371–394, ISBN 1608-280X, 1998.
Chian, A. C. L., Borotto, F. A., and Gonzalez, W. D.: Alfvén Intermittent Turbulence Driven by Temporal Chaos, Astrophys. J., 505, 993, https://doi.org/10.1086/306214, 1998.
Chian, A. C. L., Borotto, F. A., Hada, T., Miranda, R. A., Muñoz, P. R., and Rempel, E. L.: Nonlinear dynamics in space plasma turbulence: Temporal stochastic chaos, Rev. Mod. Plasma Phys., 6, 34, https://doi.org/10.1007/s41614-022-00095-z, 2022.
De Keyser, J.: Least-squares multi-spacecraft gradient calculation with automatic error estimation, Ann. Geophys., 26, 3295–3316, https://doi.org/10.5194/angeo-26-3295-2008, 2008.
De Keyser, J., Darrouzet, F., Dunlop, M. W., and Décréau, P. M. E.: Least-squares gradient calculation from multi-point observations of scalar and vector fields: methodology and applications with Cluster in the plasmasphere, Ann. Geophys., 25, 971–987, https://doi.org/10.5194/angeo-25-971-2007, 2007.
Denton, R. E., Torbert, R. B., Hasegawa, H., Dors, I., Genestreti, K. J., Argall, M. R., Gershman, D., Le Contel, O., Burch, J. L., Russell, C. T., Strangeway, R. J., Giles, B. L., and Fischer, D.: Polynomial reconstruction of the reconnection magnetic field observed by multiple spacecraft, J. Geophys. Res.-Space, 125, e2019JA027481, https://doi.org/10.1029/2019JA027481, 2020.
Dong, X.-C., Dunlop, M. W., Wang, T.-Y., Cao, J.-B., Trattner, K. J., Bamford, R., Russell, C. T., Bingham, R., Strangeway, R. J., Fear, R. C., Giles, B. L., and Torbert, R. B.: Carriers and sources of magnetopause current: MMS case study, J. Geophys. Res.-Space, 123, 5464–5475, https://doi.org/10.1029/2018JA025292, 2018.
Dunlop, M. W., Balogh, A., and Glassmeier, K.-H.: Four-point Cluster application of magnetic field analysis tools: The discontinuity analyzer, J. Geophys. Res., 107, 1385, https://doi.org/10.1029/2001JA005089, 2002a.
Dunlop, M. W., Balogh, A., Glassmeier, K.-H., and Robert, P.: Four-point cluster application of magnetic field analysis tools: The curlometer, J. Geophys. Res., 107, 1384, https://doi.org/10.1029/2001JA005088, 2002b.
Escoubet, C. P., Schmidt, R., and Goldstein, M. L.: Cluster–Science and mission overview, Space Sci. Rev., 79, 11–32, https://doi.org/10.1023/A:1004923124586, 1997.
Escoubet, C. P., Fehringer, M., and Goldstein, M.:
Introduction The Cluster mission, Ann. Geophys., 19, 1197–1200, https://doi.org/10.5194/angeo-19-1197-2001, 2001.
Haaland, S., Hasegawa, H., Paschmann, G., Sonnerup, B., and Dunlop, M.: 20 years of Cluster observations: The magnetopause, J. Geophys. Res., 126, JA029362, e2021, https://doi.org/10.1029/2021JA029362, 2021.
Hamrin, M., Rönnmark, K., Börlin, N., Vedin, J., and Vaivads, A.: GALS – Gradient Analysis by Least Squares, Ann. Geophys., 26, 3491–3499, https://doi.org/10.5194/angeo-26-3491-2008, 2008.
Harvey, C. C.: Spatial gradients and the volumetric tensor, in: Analysis methods for multi-spacecraft data, edited by: Paschmann, G. and Daly, P. W., European Space Agency Publ. Division, Noordwijk, the Netherlands, 307–322, ISBN 1608-280X, 1998.
Kieokaew, R., Foullon, C., and Lavraud, B.: Four-Spacecraft Magnetic Curvature and Vorticity Analyses on Kelvin-Helmholtz Waves in MHD Simulations, J. Geophys. Res., 123, 513–529, https://doi.org/10.1002/2017JA024424, 2018.
Kieokaew, R. and Foullon, C.: Kelvin-Helmholtz Waves Magnetic Curvature and Vorticity: Four-Spacecraft Cluster Observations, J. Geophys. Res., 124, 3347–3359, https://doi.org/10.1029/2019JA026484, 2019.
Liu, Y. Y., Fu, H. S., Olshevsky, V., Pontin, D. I., Liu, C. M., Wang, Z., Chen, G., Dai, L., and Retino, A.: SOTE: A nonlinear method for magnetic topology reconstruction in space plasmas, Astrophys. J., 244, 31, https://doi.org/10.3847/1538-4365/ab391a, 2019.
Lundquist, S.: Magnetohydrostatic fields, Ark. Fys., 2, 361–365, 1950.
Pecora, F., Yang, Y., Matthaeus, W. H., Chasapis, A., Klein, K. G., Stevens, M., Servidio, S., Greco, A., Gershman, D. J., Giles, B. L., and Burch, J. L.: Three-Dimensional Energy Transfer in Space Plasma Turbulence from Multipoint Measurement, Phys. Rev. Lett., 131, 225201, https://doi.org/10.1103/PhysRevLett.131.225201, 2023.
Politano, H. and Pouquet, A.: Von Kármán–Howarth equation for magnetohydrodynamics and its consequences on third-order longitudinal structure and correlation functions, Phys. Rev. E., 57, R21–R24, https://doi.org/10.1103/PhysRevE.57.R21, 1998a.
Politano, H. and Pouquet, A.: Dynamical length scales for turbulent magnetized flows, Geophys. Res. Lett., 25, 273–276, https://doi.org/10.1029/97GL03642, 1998b.
Retinò, A., Khotyaintsev, Y., Le Contel, O., Marcucci, M. F., Plaschke, F., Vaivads, A., Angelopoulos, V., Blasi, P., Burch, J., De Keyser, J., Dunlop, M., Dai, L., Eastwood, J., Fu, H., Haaland, S., Hoshino, M., Johlander, A., Kepko, L., Kucharek, H., Lapenta, G., Lavraud, B., Malandraki, O., Matthaeus, W., McWilliams, K., Petrukovich, A., Pinçon, J.-L., Saito, Y., Sorriso-Valvo, L., Vainio, R., and Wimmer-Schweingruber, R.: Particle energization in space plasmas: towards a multi-point, multi-scale plasma observatory, Exp. Astron., 54, 427–471, https://doi.org/10.1007/s10686-021-09797-7, 2022.
Robert, P., Roux, A., Harvey, C. C., Dunlop, M. W., Daly, P. W., and Glassmeier, K.-H.: Tetrahedron geometric factors, in: Analysis methods for multi-spacecraft data, edited by: Paschmann, G. and Daly, P. W., European Space Agency Publ. Division, Noordwijk, the Netherlands, 323–348, ISBN 1608-280X, 1998.
Rong, Z. J., Wan, W. X., Shen, C., Li, X., Dunlop, M. W., Petrukovich, A. A., Zhang, T. L., and Lucek, E.: Statistical survey on the magnetic structure in magnetotail current sheets, J. Geophys. Res., 116, A09218, https://doi.org/10.1029/2011JA016489, 2011.
Runov, A., Sergeev, V. A., Nakamura, R., Baumjohann, W., Apatenkov, S., Asano, Y., Takada, T., Volwerk, M., Vörös, Z., Zhang, T. L., Sauvaud, J.-A., Rème, H., and Balogh, A.: Local structure of the magnetotail current sheet: 2001 Cluster observations, Ann. Geophys., 24, 247–262, https://doi.org/10.5194/angeo-24-247-2006, 2006.
Russell, C. T., Mellott, M. M., Smith, E. J., and King, J. H.: Multiple spacecraft observations of interplanetary shocks: Four spacecraft determination of shock normals, J. Geophys. Res., 88, 4739–4748, https://doi.org/10.1029/JA088iA06p04739, 1983.
Shen, C., Li, X., Dunlop, M., Liu, Z. X., Balogh, A., Baker, D. N., Hapgood, M., and Wang, X.: Analyses on the geometrical structure of magnetic field in the current sheet based on cluster measurements, J. Geophys. Res., 108, 1168, https://doi.org/10.1029/2002JA009612, 2003.
Shen, C., Liu, Z. X., Li, X., Dunlop, M., Lucek, E., Rong, Z. J., Chen, Z. Q., Escoubet, C. P., Malova, H. V., Lui, A. T. Y., Fazakerley, A., Walsh, A. P., and Mouikis, C.: Flattened current sheet and its evolution in substorms, J. Geophys. Res., 113, A07S21, https://doi.org/10.1029/2007JA012812, 2008.
Shen, C., Rong, Z. J., Dunlop, M. W., Ma, Y. H., Li, X., Zeng, G., Yan, G. Q., Wan, W. X., Liu, Z. X., Carr, C. M., and Rème, H.: Spatial gradients from irregular, multiple-point spacecraft configurations, J. Geophys. Res., 117, A11207, https://doi.org/10.1029/2012JA018075, 2012.
Shen, C., Yang, Y. Y., Rong, Z. J., Li, X., Dunlop, M., Carr, C. M., Liu, Z. X., Baker, D. N., Chen, Z. Q., Ji, Y., and Zeng, G.: Direct calculation of the ring current distribution and magnetic structur
e seen by Cluster during geomagnetic storms, J. Geophys. Res., 119, 2458–2465, https://doi.org/10.1002/2013JA019460, 2014.
Shen, C., Zeng, G., Zhang, C., Rong, Z., Dunlop, M., Russell, C. T., Escoubet, C. P., and Ren, N.: Determination of the configurations of boundaries in space, J. Geophys. Res., 125, JA028163, https://doi.org/10.1029/2020JA028163, 2020.
Shen, C., Zhang, C., Rong, Z., Pu, Z., Dunlop, M. W., Escoubet, C. P., Russell, C. T., Zeng, G., Ren, N., Burch, J. L., and Zhou, Y.: Nonlinear magnetic gradients and complete magnetic geometry from multispacecraft measurements, J. Geophys. Res., 126, JA028846, https://doi.org/10.1029/2020JA028846, 2021a.
Shen, C., Zhou, Y. F., Ma, Y. H., Wang, X. G., Pu, Z. Y., and Dunlop, M.: A general algorithm for the linear and quadratic gradients of physical quantities based on 10 or more point measurements, J. Geophys. Res., 126, JA029121, https://doi.org/10.1029/2021JA029121, 2021b.
Shi, J. K., Cheng, Z. W., Zhang, T. L., Dunlop, M., Liu, Z. X., Torkar, K., Fazakerley, A., Lucek, E., Rème, H., Dandouras, I., Lui, A. T. Y., Pu, Z. Y., Walsh, A. P., Volwerk, M., Lahiff, A. D., Taylor, M. G. G. T., Grocott, A., Kistler, L. M., Lester, M., Mouikis, C., and Shen, C.: South-north asymmetry of field-aligned currents in the magnetotail observed by Cluster, J. Geophys. Res., 115, A07228, https://doi.org/10.1029/2009JA014446, 2010.
Shi, Q. Q., Shen, C., Pu, Z. Y., Dunlop, M. W., Zong, Q. G., Zhang, H., Xiao, C. J., Liu, Z. X., and Balogh, A.: Dimensional analysis of observed structures using multipoint magnetic field measurements: Application to Cluster, Geophys. Res. Lett., 32, L12105, https://doi.org/10.1029/2005GL022454, 2005.
Sonnerup, B. U. Ö., Haaland, S., Paschmann, G., Lavraud, B., Dunlop, M. W., Rème, H., and Balogh, A.: Orientation and motion of a discontinuity from single-spacecraft measurements of plasma velocity and density: Minimum mass flux residue, J. Geophys. Res., 109, A03221, https://doi.org/10.1029/2003JA010230, 2004.
Torbert, R. B., Dors, I., Argall, M. R., Genestreti, K. J., Burch, J. L., Farrugia, C. J., Forbes, T. G., Giles, B. L., and Strangeway, R. J.: A new method of 3-D magnetic field reconstruction, Geophys. Res. Lett., 47, GL085542, https://doi.org/10.1029/2019GL085542, 2020.
Vogt, J., Albert, A., and Marghitu, O.: Analysis of three-spacecraft data using planar reciprocal vectors: methodological framework and spatial gradient estimation, Ann. Geophys., 27, 3249–3273, https://doi.org/10.5194/angeo-27-3249-2009, 2009.
Vogt, J., Sorbalo, E., He, M., and Blagau, A.: Gradient estimation using configurations of two or three spacecraft, Ann. Geophys., 31, 1913–1927, https://doi.org/10.5194/angeo-31-1913-2013, 2013.
Yang, Y.: Energy Transfer and Dissipation in Plasma Turbulence: From Compressible MHD to Collisionless Plasma, Springer Theses, Springer Singapore, https://doi.org/10.1007/978-981-13-8149-2, 2019.
Zhang, Q.-H., Dunlop, M. W., Lockwood, M., Holme, R., Kamide, Y., Baumjohann, W., Liu, R.-Y., Yang, H.-G., Woodfield, E. E., Hu, H.-Q., Zhang, B.-C., and Liu, S.-L.: The distribution of the ring current: Cluster observations, Ann. Geophys., 29, 1655–1662, https://doi.org/10.5194/angeo-29-1655-2011, 2011.
Zhou, Y. and Shen, C.: Estimating gradients of physical fields in space, Ann. Geophys., 42, 17–28, https://doi.org/10.5194/angeo-42-17-2024, 2024.
