Alfven speed MHD magnetohydrodynamics calculator

The Alfven speed calculator determines the propagation velocity of transverse magnetohydrodynamic (MHD) waves (Alfven mode) along magnetic field lines in a magnetized plasma, from magnetic field B and plasma mass density ρ, following the formulation by Swedish physicist Hannes Alfven 1942 Nature "Existence of Electromagnetic-Hydrodynamic Waves" (vol. 150, p. 405) Royal Institute of Technology Stockholm, founder of magnetohydrodynamics MHD, Nobel Prize in Physics 1970 "for fundamental work and discoveries in magnetohydrodynamics with fruitful applications in different parts of plasma physics". The classical formula: v_A = B / √(μ₀·ρ) [m/s], where B = magnetic field magnitude in Tesla, μ₀ = 4π×10⁻⁷ T·m/A vacuum magnetic permeability, ρ = plasma mass density in kg/m³. For a fully ionized hydrogen plasma: ρ = n·m_p (n = proton number density m⁻³, m_p = 1.673×10⁻²⁷ kg proton mass). The Alfvenic Mach number M_A = v/v_A characterizes regime: MHD wave stability requires M_A < 1 (sub-Alfvenic). The Alfven time τ_A = L/v_A represents crossing time of characteristic length L. The 4 plasma categories:

• Diffuse astrophysical plasma (solar corona, solar wind, ISM) v_A 10-1000 km/s
• Laboratory fusion plasma (tokamak ITER, FTU, DTT) v_A 1000-10000 km/s
• Magnetospheric plasma (Earth, Jupiter, Mercury) v_A 100-1000 km/s
• Compact extreme plasma (pulsars, magnetars, AGN accretion disks) v_A → c relativistic. Main MHD applications:

• Magnetohydrodynamics coupled Maxwell + Navier-Stokes equations
• Solar physics coronal reconnection, flares, CME, helioseismology
• Tokamak MHD instability sawtooth, ELMs, kink modes ITER
• Solar wind propagation Alfven wave acceleration
• Magnetosphere substorm dynamics tail reconnection
• Pulsar/Magnetar emission relativistic magnetospheres
• Galactic dynamo amplification α-Ω MHD turbulence
• Accretion disks AGN/X-ray binaries MRI Magnetorotational Instability Balbus-Hawley 1991
• Magnetic reconnection Sweet-Parker 1958, Petschek 1964 fast reconnection. Italian applications:

• ENEA Frascati DTT Divertor Tokamak Test 2028 + FTU Frascati Tokamak Upgrade 1989-2020 magnetic fusion plasma
• Solar Orbiter ESA 2020 ASI 25% magnetic field MAG + Solar Wind Analyser SWA Italian INAF instrument Alfven waves corona-heliosphere
• BepiColombo ESA-JAXA 2018 ASI 35% magnetometer MMO ISA Mercury magnetosphere
• ITER Cadarache France 2025 + Ansaldo Nucleare Genoa engineering 500 MW fusion plasma
• INAF IAPS Rome plasma physics + INAF Trieste 1898 IBIS solar physics
• Cineca Marconi100 + Leonardo Bologna MHD simulations pulsars accretion disks

Italian Alfven speed reference table

(Source: Hannes Alfven 1942 Nature vol. 150 p. 405 + Nobel Prize Physics 1970 + ENEA Frascati DTT/FTU + Solar Orbiter ESA 2020 ASI + BepiColombo ESA-JAXA 2018 + ITER Cadarache 2025 + INAF IAPS Rome data).

Italian Alfven speed examples

• Quiet solar corona Solar Orbiter ESA 2020 ASI 25% INAF MAG SWA: B = 10⁻³ T = 10 Gauss typical coronal loop, n = 10¹⁵ m⁻³ ionized hydrogen (ρ = n·m_p = 1.67×10⁻¹² kg/m³). v_A = B/√(μ₀·ρ) = 10⁻³/√(4π×10⁻⁷·1.67×10⁻¹²) = 6.9×10⁵ m/s ≈ 700 km/s. Sub-Alfvenic regime (solar wind 400 km/s < v_A) → coronal reconnection flares CME (Coronal Mass Ejection)
• Solar wind 1 AU Solar Orbiter MAG INAF Trieste 1898: B = 5 nT, n = 5×10⁶ m⁻³ protons (ρ = 8.4×10⁻²¹ kg/m³). v_A ≈ 50 km/s. Super-Alfvenic regime (v_sw=400-700 km/s >> v_A) → bow shock Earth magnetosphere
• ITER Cadarache France 2025 + Ansaldo Nucleare Genoa engineering: B = 5 T (Nb₃Sn superconducting toroidal), n = 10²⁰ m⁻³ deuterium-tritium (ρ = 4.17×10⁻⁷ kg/m³ DT). v_A = 5/√(4π×10⁻⁷·4.17×10⁻⁷) ≈ 6900 km/s (DT) or 9500 km/s (H only). Sub-Alfvenic regime MHD stability ELMs sawtooth
• ENEA Frascati DTT Divertor Tokamak Test 2028 fusion plasma: B = 6 T, n = 2×10²⁰ m⁻³, ρ = 3.3×10⁻⁷ kg/m³. v_A ≈ 9400 km/s. ENEA Frascati 1959 + DTT 600 M€ PNRR investment
• Earth magnetosphere plasmasphere Cluster ESA + INAF IAPS Rome: B = 3×10⁻⁴ T = 30000 nT (equatorial surface), n = 10⁸ m⁻³ hydrogen (ρ = 1.67×10⁻¹⁹ kg/m³). v_A ≈ 1000 km/s in plasmasphere n=10⁹ m⁻³. Substorm regime tail reconnection
• Mercury magnetosphere BepiColombo ESA-JAXA 2018 ASI 35% MMO ISA: B ≈ 250 nT (weak intrinsic field 1% Earth), n = 10⁷ m⁻³ solar wind. v_A ≈ 30 km/s. Mini-Earth magnetosphere + FTE Flux Transfer Events reconnection
• AGN accretion disk M87 Sgr A* INAF IAPS: B = 10⁻⁴ T, n = 10¹⁵ m⁻³ ionized. v_A ≈ 70 km/s. MRI Magnetorotational Instability Balbus-Hawley 1991 α-viscosity disk turbulence
• Crab Vela pulsar magnetosphere INAF Bologna AGILE ASI 2007: B = 10⁸ T (10¹² Gauss surface), n = 10²⁰ m⁻³ pair plasma e+/e-. v_A → c relativistic polar cap radio emission curvature radiation

Italian MHD plasma astrophysics

Italian MHD plasma astrophysics:

• ENEA Frascati 1959 (Italian National Agency for Alternative Energy): FTU Frascati Tokamak Upgrade 1989-2020 8 T toroidal magnetic fusion plasma record q ≈ 1; DTT Divertor Tokamak Test 2028 6 T 6 MA plasma liquid metal divertor 600 M€ PNRR Mission 2 investment; EUROfusion + ITER collaboration
• INFN Frascati 1957 LNF Frascati National Laboratories: DAFNE φ-factory accelerator 1999; Carlo Rubbia 1984 CERN Nobel W Z bosons + ICARUS Gran Sasso liquid argon TPC neutrinos
• ITER Cadarache France 2025 + Ansaldo Nucleare Genoa engineering: 500 MW fusion plasma DT 150 M K, Nb₃Sn 11.5 T toroidal + 6 T poloidal magnets; ENEA + RFX Padua partnership 1.7 B€ Italian contribution
• INAF Italian National Astrophysics Institute Rome 2002 Monte Porzio Catone (16 observatories, 1700 researchers): Trieste 1898 IBIS Interferometric Bidimensional Spectrometer solar physics Alfven waves; IAPS Astrophysics and Space Planetology Institute Rome plasma physics magnetospheres; Padua 1761; Brera Milan 1762; Capodimonte Naples 1812; Arcetri Florence 1872; Rome 1786; Catania-Etna 1880; Bologna Loiano 1936; Palermo 1790; Cagliari 1899 SRT 64 m
• Italian magnetic plasma missions ASI Rome 1988: Solar Orbiter ESA 2020 ASI 25% magnetometer MAG + Solar Wind Analyser SWA INAF Alfven waves corona-heliosphere (perihelion 0.28 AU); BepiColombo ESA-JAXA 2018 ASI 35% magnetometer MMO MIO Italian Spring Accelerometer ISA Mercury magnetosphere arrival 2026; AGILE satellite ASI 2007 Astrorivelatore Gamma Immagini LEggero Crab Vela pulsar magnetosphere; INTEGRAL ESA 2002 INAF magnetar SGR 1806 GRB; LiteBIRD ESA 2032 INAF + ASI CMB B-modes inflation primordial MHD; Athena ESA 2035 X-IFU INAF Palermo 25% X-ray plasma cluster ICM accretion disks
• Pierre Auger Observatory Argentina (INFN + INAF) UHECR cosmic rays > 10²⁰ eV intergalactic MHD propagation
• ICTP Trieste 1964 + SISSA Trieste 1978 astrophysical plasma (Massimo Stiavelli STScI ex-INAF, Andrea Lapi SISSA AGN MHD accretion disks)
• Cineca Casalecchio Bologna 1969 Marconi100 30 PFlops + Leonardo HPC pre-exascale 250 PFlops 2023 (5th TOP500 worldwide) MHD pulsar magnetosphere turbulence galactic dynamo simulations
• INFN-LNS Catania K800 cyclotron nuclear laboratory plasma
• Italian Physics Nobel Prizes: Marconi 1909, Fermi 1938, Segre 1959, Carlo Rubbia 1984, Giacconi 2002 X-ray. Italian R&D incentives 2025: R&D Tax Credit art. 1 c. 200 L. 160/2019 up to 25% (MHD plasma); Patent Box L. 178/2020 50%; Industry/Transition 5.0 Tax Credit art. 38 DL 39/2024 up to 35%; PNRR Mission 2 hydrogen-fusion 3.2 B€ + Mission 4 research 6.9 B€

Updated July 2026