MRI Magnets and Coils — Deep Reference

A clinical 3 T MRI scanner is the largest superconducting magnet most engineers will ever see in person — 4–6 tonnes of NbTi conductor in a 70 cm bore, persistent-current-mode at $\sim$5 kA winding current, 1.5 km of helium-cooled wire, and a fringe field that requires a 100 m exclusion zone for cardiac pacemakers. A 7 T research scanner adds Nb${}_3$Sn high-field coils, dynamic shimming, and 64-channel RF receive arrays. A 0.5 T point-of-care portable (Hyperfine Swoop) replaces the cryostat with a permanent-magnet Halbach array and the gradient amplifiers with 1 kW Class-D PWM stages — taking the price from $15M to under $300k but with proportionally lower SNR. This note covers the four field-generating subsystems that make MR imaging work — the static B0 magnet, the gradient coils, the RF transmit and receive coils, and the active / passive shim system — across vendor and field-strength regimes, plus the engineering of cryogenics, quench protection, safety, and recent low-field and HTS developments.

See also

• electromagnetics-engineering
• magnetic-sensors-deep
• bioinstrumentation
• photonics
• power-electronics
• quantum-materials-and-topological-phases
• magnetic-and-optical-materials
• rf-design

0. Historical milestones

• 1946 — Bloch (Stanford) and Purcell (Harvard) independently demonstrate nuclear magnetic resonance in condensed-matter samples. Nobel Prize 1952.
• 1973 — Paul Lauterbur (SUNY Stony Brook) publishes “Image Formation by Induced Local Interactions” in Nature — the first NMR image of two water-filled tubes. Magnetic field gradients used for spatial encoding.
• 1974 — Peter Mansfield (Nottingham) introduces slice-selective excitation and line-scan imaging.
• 1977 — Damadian builds Indomitable, the first whole-body human MRI scanner; first human image (chest) on 3 July 1977.
• 1980 — First commercial MRI scanners ship (FONAR QED 80, Diasonics MR-200).
• 1981 — First superconducting MR magnets (Oxford Instruments) — replaces resistive electromagnets.
• 1991 — Functional MRI demonstrated by Ogawa, Belliveau et al — BOLD contrast.
• 1993 — First commercial 3 T clinical scanners (Bruker Tomikon S300).
• 2002 — 7 T research scanners installed at NIH and University of Minnesota CMRR.
• 2003 — Lauterbur and Mansfield share Nobel Prize in Physiology or Medicine.
• 2008 — 11.7 T animal-scale scanners installed at NIH Bethesda; first 9.4 T whole-body at CMRR.
• 2017 — Siemens MAGNETOM Terra — first FDA-cleared 7 T whole-body clinical scanner.
• 2020 — Hyperfine Swoop FDA-cleared portable 0.064 T MRI.
• 2022 — Iseult 11.7 T whole-body scanner at NeuroSpin Saclay produces first human images. United Imaging uMR Jupiter 5 T enters commercial production.

1. System map

A clinical whole-body MRI consists of (from outside in):

1. Radiofrequency shield room — 100–120 dB attenuation cage around the suite to keep external RF from coupling into the receiver.
2. Static magnet (B0) — the dominant subsystem by mass, cost, and engineering complexity. Generates the longitudinal polarising field.
3. Passive iron shimming + active gradient coils — three orthogonal coil sets ($G_x$, $G_y$, $G_z$) produce linear field variations across the imaging volume; passive iron blocks compensate static inhomogeneity.
4. Active shim coils — 1st, 2nd, and sometimes 3rd-order spherical-harmonic correction coils, driven during scan.
5. RF body coil (transmit + receive) — birdcage-type, fixed inside the bore.
6. RF receive array — 8 / 16 / 32 / 64 / 128-channel surface coil arrays placed on the patient.
7. Patient table + isocentre — table positioning to $\pm$1 mm; isocentre is the field’s homogeneity sweet spot.
8. Console + reconstruction computer — vendor-specific OS (GE Signaworks, Siemens syngo, Philips IntelliSpace) plus a GPU-accelerated recon backend.
9. Cryogen tank + chiller plant — 1500–4000 L of liquid helium, cryocooler, helium reservoirs in case of quench.

The static magnet dominates the system specification, since every other subsystem must operate compatibly with the B0 field. The gradient and RF coils each see hundreds of amps and tens of kV during a scan and must do so without disturbing B0 homogeneity below the 1 ppm level over the imaging volume.

2. Static B0 magnet — superconducting whole-body

2.0 The case for high field

Signal-to-noise ratio (SNR) of a clinical MR image scales roughly as $B_0^{7/4}$ for whole-body coil reception and faster for surface arrays — meaning a 7 T scan delivers $\sim$10× the SNR of a 1.5 T scan at the same voxel resolution. Each doubling of field roughly halves the achievable in-plane voxel size at constant scan time, or quarters the scan time at constant voxel size. Susceptibility-derived contrast (BOLD for fMRI, $T_2^{\ast }$, SWI, QSM, ${}^{31}$P MRS, ${}^{23}$Na MRI) scales linearly or faster with $B_0$, motivating ultra-high field (UHF) installations. The penalties are dielectric resonance (the body becomes electrically large at 7 T), increased SAR ($\propto B_0^2$), and exponential magnet cost.

2.1 Field strength and conductor choice

Clinical and research field strengths cluster at six values:

Field	Conductor	Coil arrangement	Typical use
0.064–0.55 T	NdFeB or Sm-Co PM	Halbach / C-arm / dipole	point-of-care, MR-Linac low
0.5 T	NbTi	low-cryogen split solenoid	extremity, open MRI
1.5 T	NbTi	persistent solenoid	clinical workhorse
3 T	NbTi	persistent solenoid	clinical premium, fMRI, neuro
7 T	Nb${}_3$Sn	actively-shielded solenoid	research neuro, ultra-high-resolution clinical
9.4 T / 11.7 T	Nb${}_3$Sn	actively-shielded + passive iron	research-only neuro
14 T / 21 T	Nb${}_3$Sn + HTS REBCO	hybrid	research-only / under construction

The critical surface for NbTi sits at $\sim$11 T at 4.2 K and $\sim$13 T at 1.9 K — adequate for 3 T whole-body but not for 7 T. Beyond 7 T whole-body, Nb${}_3$Sn (with $T_c=18$ K, $B_{c2}$ up to 28 T at 4.2 K) is required; Nb${}_3$Sn is strain-sensitive (degrades $>$ 0.3 % strain) and requires the “wind-and-react” technique — wind the magnet from copper-clad bronze precursor, then react in a 650 °C furnace for $\sim$200 hours to form the brittle A15 phase in situ.

2.2 Persistent-current mode

A clinical MRI superconducting magnet operates in persistent mode: the magnet is energised from an external power supply by ramping up the current over 1–6 hours, then a superconducting switch (a length of NbTi heated above $T_c$ when open, cooled below $T_c$ when closed) is closed across the terminals, shorting the magnet on itself. The external supply is then de-energised and disconnected, leaving the current circulating with no resistance. Decay rate $<$ 0.1 ppm/hour (the field drifts by less than $\sim 10^{-4}$ T per year on a 3 T magnet) — adequate for the scan-to-scan reproducibility MRI demands. The magnet then runs for years between ramp-downs (usually only for service or relocation).

2.3 Cryogenics

The conductor must stay below $T_c$. Two regimes:

• Bath-cooled — the entire magnet is submerged in a liquid-helium bath at 4.2 K, with the cryostat held under 1 atm of cold He gas above the liquid. Standard for 1.5 T and 3 T clinical. A 3 T magnet has a 1500–2000 L bath; helium boil-off is captured and re-liquefied by a cryocooler.
• Conduction-cooled (cryogen-free or “low-cryogen”) — a Gifford-McMahon or pulse-tube cryocooler (Cryomech, Sumitomo SHI, Siemens Magnetom variants) at 4 K is mechanically coupled to the coil former via braided copper straps. No liquid helium bath, only $\sim$5–20 L for thermal mass. The leading edge: Siemens MAGNETOM Free.Max (0.55 T whole-body with $\sim$0.7 L He), Philips Ingenia Ambition (1.5 T sealed BlueSeal magnet with 7 L He, no quench-vent), and the GE Signa MR Sigma Hero ZBO line.

The cryocooler delivers $\sim$1.5 W at 4 K. A magnet that boils off all 1500 L of helium over a 5-year service cycle, vs one with a sealed magnet and a 7 L charge, has a 200× lower lifetime helium consumption — and the latter is operable in a hospital without a 1500 L Dewar refill schedule. This is the single biggest practical change in MRI since 2018.

2.4 Quench

A quench is the catastrophic failure mode of a superconducting magnet: a small region transitions from superconducting to normal-conducting (e.g. from local heating, conductor motion, training instability), the resistive zone propagates along the conductor at 30–300 m/s, ohmic heating causes the helium to boil, the pressure spikes, and within 30–120 s the entire magnet has dumped its stored energy ($\sim$10 MJ for a 3 T whole-body) into resistive heating, vaporising 1000+ litres of helium into 700× gas volume. The cryostat vents through a 6–8 inch quench tube to the building exterior; the room itself must not asphyxiate occupants if the vent fails.

Quench-protection design:

• Persistent-mode current dump diodes — bypass paths that activate at $\sim$100 mV across coil sections to share dissipation.
• Quench heaters — strategic resistive heaters fired by the protection electronics to spread the normal zone, increase resistance, and shorten the dump time. Each heater is a 2–4 Ω wire pad pulsed at $\sim$300 V for 1–10 ms.
• Active quench protection (AQP) — software-driven heater-firing system; modern MR vendors all have proprietary AQP that adds 20–30 % of magnet cost.

A quench is a serviceable but expensive event: 10 000–60 000 USD to refill helium plus a multi-week ramp-up. Sealed-cryostat designs (Philips BlueSeal, Siemens DryCool) eliminate the helium loss but still require a multi-day re-ramp.

2.5 Active vs passive magnetic shielding

A 3 T magnet’s 5-gauss line extends roughly 10 m in unshielded form — well beyond a typical scanner suite footprint. Two countermeasures:

• Active shielding — a second concentric coil at larger radius, wound to produce an opposite dipole. Cancels the dipole moment seen externally and pulls the 5 G line in to $\sim$4 m axially / 2.5 m radially. Standard since ~1995; reduces facility cost by eliminating room-scale iron shielding.
• Passive iron shielding — adds tonnes of low-carbon steel around the suite walls. Cheaper for very-high-field (7 T and above) systems but adds $\sim$10–20 tonnes of mass to the building load.

A 7 T whole-body scanner (Siemens MAGNETOM Terra/Terra.X) typically combines both — active shielding plus 30+ tonnes of passive iron — to keep stray field manageable.

2.6 Magnet construction details

A whole-body 3 T solenoid magnet has:

• Cold mass — 4–6 tonnes of copper-stabilised NbTi wire (a $\sim$0.7 mm-diameter twisted multi-filament wire with 5000–20000 NbTi filaments embedded in Cu matrix), wound into 4–8 axial coil sections. The cold mass is suspended inside the cryostat on Kevlar / G-10 tension straps to minimise heat conduction.
• Vacuum vessel — 304 stainless-steel outer shell with multi-layer insulation (aluminised mylar, $\sim$30 layers). Vacuum 10${}^{-5}$ Pa.
• Thermal radiation shields — intermediate aluminium shields at 40 K and 80 K, conduction-cooled to intercept room-temperature radiation before it reaches 4 K.
• Cold-head interface — Sumitomo RDK-415D2 4 K cryocooler ($\sim$1.5 W at 4 K, $\sim$45 W at 40 K) re-condenses boiled-off helium. Mean time between failure: 30 000 h.
• Burst-disk safety — primary pressure relief at 80 kPa above atmospheric; opens to the quench-vent stack.
• Magnet leads — superconducting persistent-switch + retractable HTS current leads (or detachable copper leads) for the energising / de-energising connection. Retracting the leads after a successful ramp drops the heat leak from $\sim$200 mW to $\sim$5 mW.

The persistent switch is the critical piece: a 50 mm coil of NbTi wire mounted in the cold space, equipped with a tiny resistive heater. With the heater off (switch closed), the NbTi is superconducting and bridges the magnet terminals. With the heater on (switch open), the NbTi goes resistive and the external supply controls the magnet current. Switching the heater off in steady state locks the persistent loop.

2.7 Production whole-body scanners (2024–2026)

• GE HealthCare — Signa Premier 3T (60 channel, AIR Coils Suite, Spectronic AI recon), Signa Architect / Hercules 3T mid-range, MR Sigma Hero 3T no-boil-off, Voyager 1.5T, Pioneer 3T research-platform.
• Siemens Healthineers — MAGNETOM Vida 3T (XQ gradients 60/200 mT/m), MAGNETOM Cima.X 3T (Gemini gradients 200/200), MAGNETOM Free.Max 0.55T (sealed BlueSeal, helium-light), MAGNETOM Terra/Terra.X 7T (whole-body clinical 7T, single-channel pTx).
• Philips — Ingenia Elition X 3T, MR 7700 3T (XP gradient 200/200), Ingenia Ambition 1.5T BlueSeal (sealed magnet), Multiva 1.5T.
• Canon Medical Systems — Vantage Centurian 3T, Vantage Galan 3T, Vantage Orian 1.5T.
• United Imaging Healthcare — uMR 770 / uMR 880 / uMR 990 3T (DeepRecon AI denoiser), uMR Jupiter 5T (the only commercial whole-body 5 T, $\sim$2022 launch, NbTi conductor with active shielding).
• Hyperfine — Swoop 0.064T point-of-care portable MRI (permanent-magnet, no cryogen, wheels into ER / ICU).
• Promaxo — 0.064T prostate-specific MRI (single-sided permanent-magnet).
• Synaptive Medical — Evry 0.5T head-only MRI for ICU.
• Magnetica — Australian-designed compact 0.5T extremity scanner.

A premium 3 T magnet from GE / Siemens / Philips lists at $1.8–3M. A 7 T research scanner with all the trimmings (32-channel pTx, 64-channel head Rx, ASGM gradient, customisation) is $8–15M. The Hyperfine Swoop lists at $250–350k. United Imaging’s uMR Jupiter 5 T sits at $\sim$$5M.

3. Gradient coils

3.1 Function

Three orthogonal gradient coils ($G_x$, $G_y$, $G_z$) produce field variations linear in position across the imaging volume:

$B_z(\mathbf{r})=B_0+G_{x}x+G_{y}y+G_{z}z$

The gradient encodes spatial position into the Larmor frequency of the precessing magnetisation: each voxel resonates at $\omega (\mathbf{r})=\gamma (B_0+\mathbf{G}\cdot \mathbf{r})$, and Fourier-decoding the received signal gives the spatial image. Gradients are switched at 1–10 kHz during a scan, with peak amplitudes 30–80 mT/m on clinical systems and up to 300 mT/m on research scanners.

3.2 Active and passive shielding

The gradient coils sit inside the bore, just outside the body-RF coil and just inside the magnet inner radius. They generate switching fields that couple to the magnet’s cold-mass and would induce eddy currents in the cryostat that lag behind the gradient command — destroying spatial accuracy. Modern gradients are actively shielded: a second outer coil layer cancels the field in the cryostat region. Eddy-current residuals are then trimmed with pre-emphasis filtering on the gradient amplifier output.

Passive (RF) shielding around the gradient (a copper cylinder between gradient and patient bore) blocks the RF transmit field from reaching the gradient and inducing high-frequency eddy currents.

3.3 Coil geometry — fingerprint and saddle

Two geometries dominate the active-shielded gradient coil:

• Maxwell pair for $G_z$ — two coaxial loops of opposite polarity separated by $\sqrt{3}r$ along the axis produce a perfectly linear $z$-gradient at the centre. The actual production coil uses many distributed turns to extend linearity over the imaging volume.
• Golay (saddle) coils for transverse $G_x$ and $G_y$ — four arc-shaped coils on the cylinder surface produce a transverse gradient. The standard target-field design (Turner 1986) gives the wire layout for a desired linearity over a specified DSV.

Each coil is wound from $\sim$3–8 mm copper rectangular conductor with $\sim$2 kV inter-turn insulation rating. The active shield is a second outer winding designed by the stream-function method to null the external field at the cryostat radius. Wire layout is optimised by SVD-truncated inverse-field synthesis (Stochastic-FEA in Magnet Designer software, Comsol AC/DC, custom in-house tools from Tesla Engineering UK, Siemens, GE).

3.4 Gradient amplifier

The gradient amplifier (GPA — gradient power amplifier) is the most stressed power-electronics subsystem in MRI: $\sim$2 kV bus, 1000 A peak, switching at 5–50 kHz, 50 kVA per axis. Architectures:

• PWM IGBT H-bridge — early 2000s; switching frequency 5–10 kHz; uses an LC output filter to smooth the current waveform.
• PWM SiC H-bridge — 2018+; switching 50 kHz, smaller output filter, lower losses. Resonance Research, IECO Electric, and Bruker BioSpin all use SiC modules.
• Multilevel inverter — series-stacked half-bridges; reduces $dV/dt$ on the coil. Standard on Siemens XQ/XR/Gemini gradients.

Each axis has its own GPA cabinet ($\sim$1.5 m${}^3$, $\sim$200 kg). Cooling is typically deionised-water chilled to 20 °C, $\sim$30 L/min per axis.

3.5 Slew rate and PNS limits

The gradient amplifier (a 2 kV / 1000 A H-bridge from IECO, Resonance Research, or vendor in-house) drives the coil with peak slew rates of 100–300 T/m/s. Higher slew = faster echo-train acquisition and shorter scans. But the time-varying $dB/dt$ at the patient periphery induces eddy currents in muscle and nerve tissue:

• PNS (peripheral nerve stimulation) — the limit at which subjects feel involuntary muscle twitches. ~20 T/s of peripheral $dB/dt$ corresponds to PNS threshold.
• CNS / cardiac stimulation — much higher threshold; the FDA / IEC limits keep operation 3× below it.

The IEC 60601-2-33 limits gradient $dB/dt$ to keep below PNS in routine (“normal”) mode; first-level controlled-operating-mode (CLO) allows PNS-rate operation with informed consent. Modern Cima.X / MR 7700-class systems operate near the PNS ceiling, with 200 mT/m amplitude and 200 T/m/s slew. The HCP / Connectome gradient (Magnetom Connectom 3T at NIH) goes to 300 mT/m for diffusion MRI; subjects feel transient twitches during high-b imaging.

3.6 Acoustic noise

Gradient coils sit in $B_0=1.5$–7 T. Switching 800 A in the coil produces tens of kN of Lorentz force on the conductor — the coil mechanically deflects on each pulse and radiates acoustic noise from 80 to 120 dB SPL inside the bore (a jackhammer at 1 m is $\sim$100 dB). Mitigations:

• Vacuum-sealed gradient enclosure (Philips dStream “Quiet Suite”, Siemens “GC FastDESIGN”) — pulls $\sim$5 mbar vacuum around the gradient, drops acoustic radiation by 10–20 dB.
• Active noise cancellation in headphones during scan.
• Quiet-sequence design — gradient-balanced encoding patterns that reduce mechanical loading (GE Silent Scan, Siemens Quiet Suite, Philips ComforTone).

4. RF coils

4.1 Transmit (Tx) body coil

The body coil sits inside the gradient. A birdcage topology — N identical rungs connected at top and bottom by ring capacitor segments — resonates at the Larmor frequency (63.87 MHz at 1.5 T, 127.74 MHz at 3 T, 297.21 MHz at 7 T for ${}^1$H). The birdcage’s circularly-polarised mode produces a uniform transverse B1 field across the bore — the standard transmit element since the late 1980s. Sixteen-rung high-pass and low-pass variants are typical.

At 7 T and above, the body birdcage’s wavelength (1 m in tissue at 297 MHz) becomes comparable to the body cross-section, and standing-wave artifacts (“dielectric resonance”) produce large flip-angle inhomogeneity. Parallel-transmit (pTx) systems drive each rung with an independent amplifier and phase / amplitude, using B1 mapping to shim the transmit field per slice. Siemens, Philips, GE all ship pTx-capable 7 T systems; 8- and 16-channel transmit are standard.

4.2 Receive (Rx) array

The Rx side is dominated by surface arrays — many small coils placed close to the body (or head) to maximise SNR (which scales with $\sqrt{N_{\mathrm{channels}}}$ for a properly-decoupled array). Channel counts:

Body part	Typical channels (Rx)
Whole-body	64–128
Head	32 / 48 / 64
Cardiac	16 / 32 / 64
Spine	16 / 32
Knee	8 / 16 / 18
Wrist	8 / 16

Each channel has its own preamp at the coil (the LNA — low-noise amplifier, typically a GaAs FET with $\sim$0.4 dB NF) and runs over a coax to the receiver. SNR depends on coil decoupling (mutual-inductance cancellation between adjacent loops at the geometric overlap, plus low-impedance preamp decoupling).

Major coil vendors:

• Nova Medical (Wilmington, MA) — leading 7 T head and torso arrays (32-channel head, 8-channel pTx, 32-channel cardiac).
• MR Coils BV (Netherlands / Univ. Utrecht) — custom 7 T and 9.4 T research coils, dipole arrays for body imaging.
• RAPID Biomedical (Würzburg, Germany) — Tx/Rx coils for animal MR (Bruker BioSpec) plus human 7 T research.
• GE HealthCare AIR Coils — flexible drape-style 16/30/48 channel coils that conform to body habitus.
• Siemens BioMatrix — bed-integrated body coil sets.
• Philips dStream — coil-side digitisation (each LNA output goes straight to ADC inside the coil), reducing coax noise pickup.
• MR Solutions / Quality Electrodynamics (QED, now Canon) — premium clinical coil supplier.

4.3 RF power amplifier (RFPA)

The RFPA drives the body coil at the Larmor frequency:

• 1.5 T (64 MHz): 18–25 kW peak, 1 kW average. NXP MRF6V class LDMOS modules combined in N-way Wilkinson combiners. Vendors: Communications & Power Industries (CPI), Analogic, Dressler, Continental Electronics.
• 3 T (128 MHz): 30–45 kW peak. Same LDMOS technology, higher device count.
• 7 T (300 MHz): 4–8 kW per channel, 8–16 channels in pTx. Each channel is a 1.5 kW LDMOS amplifier with its own real-time waveform control.

A 30 kW peak RFPA pulse has a duty cycle $<$ 10 % and average power $<$ 3 kW. The amplifier output goes through a Tx/Rx switch (PIN-diode T/R, with 60 dB isolation) and into the body coil’s matching network.

4.4 SAR limits

RF transmit power deposited in tissue heats it. Specific absorption rate (SAR, W/kg) is limited by IEC 60601-2-33:

• Whole-body SAR — 2 W/kg averaged over any 6-minute window (normal mode); 4 W/kg first-level CLO.
• Head SAR — 3.2 W/kg averaged 6 min.
• Local SAR — 10 W/kg over any 10 g of tissue.

A typical 3 T turbo-spin-echo (TSE) sequence at high flip angle approaches the whole-body limit; the scanner re-paces ETL or TR to stay below. At 7 T pTx the local SAR can spike 4–10× higher than the body coil, so per-channel SAR monitoring is mandatory and on every scan the safety-monitoring loop runs the virtual-observation-point model against the patient’s body geometry.

4.5 Coil decoupling techniques

When N receive coils overlap and share an imaging volume, mutual inductance between elements destroys the SNR benefit unless they are decoupled. Three techniques:

• Geometric decoupling — overlap adjacent coils by the magic distance ($\sim$30 % of the loop diameter for circular loops) at which the net mutual flux is zero. The Roemer-original phased-array decoupling method.
• Preamp decoupling — each loop is loaded with a low-impedance input preamp (typically $\sim$2 Ω at 64 / 128 / 300 MHz) that effectively shorts the loop and prevents current circulation from neighbours. Standard since the 1990s.
• Counter-wound decoupling — adjacent loops connected by a counter-wound trace that injects an opposing voltage, cancelling the induced EMF from the neighbour. Used in tight-pitched 128-channel arrays where geometric overlap is impractical.

For dipole-style 7 T body arrays (Nova Medical, MR Coils BV), decoupling is even harder: the dipole’s far-field coupling is much larger than a loop’s near-field coupling. Designs use λ/2 dipoles separated by combination geometric + preamp + capacitive-bridge decoupling.

5. Shimming

A clinical magnet at the factory is shimmed to $\sim$1 ppm over a 50 cm sphere; on-site, additional shimming brings it to $\sim$0.1 ppm. Three layers:

5.1 Passive shim

Small ferromagnetic blocks (iron, $\sim$30–80 g each) placed in $\sim$30 axially-distributed trays around the bore correct the static field’s spherical-harmonic deviations from uniform. Set once at install + re-trim every 1–3 years. Field-mapped with a Bartington fluxgate or vendor B0-field-mapping cart.

5.2 Active shim coils — first to third order

Spherical-harmonic shim coils are wound into the gradient assembly. They produce field variations $B_z=\sum c_{nm}{Y}_{nm}(\theta ,\varphi )$:

• 0th order — uniform field (frequency offset, $\Delta f$).
• 1st order — $x$, $y$, $z$ linear gradients (same as imaging gradients).
• 2nd order — $xy$, $xz$, $yz$, $z^2$, $x^2-y^2$ (5 coils).
• 3rd order — 7 more coils (optional, on premium systems).

Each coil is driven by a $\sim$10 A DC supply during the scan. Dynamic shimming updates the shim currents per slice for body imaging (where $B_0$ inhomogeneity varies slice-to-slice).

5.3 Spherical harmonic budget

Shim performance is reported as residual $B_0$ inhomogeneity in ppm peak-to-peak over a defined volume of interest. Specifications:

Volume	Field	Typical residual after shim
10 cm DSV	3 T	0.05 ppm (HC) / 0.1 ppm (clinical)
25 cm DSV	3 T	0.5 ppm
40 cm DSV	3 T	1.0 ppm
50 cm DSV	3 T	2.0 ppm
10 cm DSV	7 T	0.1 ppm (with dynamic shim)

Each ppm of inhomogeneity at 3 T equals 128 Hz of ${}^1$H frequency spread; sequences with long readouts (EPI) or strong gradient encoding (spiral) are most sensitive.

5.4 fMRI-grade real-time shim

The premium ASGM (advanced shim gradient module) on Siemens MAGNETOM Terra.X and Philips MR 7700 actively updates the shim during the scan from a real-time B0 map. Important for high-resolution functional MRI where 0.05 ppm field drift visible as a slow signal modulation can dominate task activation.

6. Low-field and portable MRI

6.1 Hyperfine Swoop

A 0.064 T (64 mT) permanent-magnet Halbach-array MRI on wheels, sub-2-tonne footprint, plugs into a standard outlet. Targeted at ICU and ED point-of-care neuroimaging where transporting a critical patient to a fixed scanner is infeasible. SNR is $\sim$50× worse than 3 T per voxel, but AI image-reconstruction (Hyperfine’s “AI-Powered Imaging” — a learned-prior reconstruction trained on paired 3 T / 0.064 T data) recovers diagnostically-usable contrast. FDA clearance since 2020; > 50 hospitals operating units by 2025. Cost $250–350k.

6.2 Promaxo

A 0.064 T single-sided MRI for transperineal prostate biopsy guidance. The magnet is C-arm-shaped with one open side facing the patient; only the prostate region is in the homogeneity zone. Eliminates the cost-and-throughput problem of fitting biopsies into a busy 3 T schedule. FDA 510(k) since 2022.

6.3 Synaptive Evry

A 0.5 T helmet-only head MRI for ICU neuroimaging. Lower-field neuro is dramatically easier on susceptibility-artifact at brain-bone interfaces. Synaptive bundles surgical planning + intraoperative imaging.

6.4 Magnetica

Australian compact extremity scanners (wrist, knee, elbow), 0.5 T cryogen-free, $\sim$$400k installed.

6.5 Halbach permanent-magnet array

A Halbach cylinder is a hollow ring of permanent magnet segments whose magnetisation rotates by $2\theta$ as the azimuth $\theta$ advances around the ring. The result: an ideal Halbach cylinder produces a perfectly uniform transverse field inside the bore and zero field outside. With $K$ azimuthal segments of finite width and arc-length, the discrete approximation reaches 1000–5000 ppm bore uniformity at 0.05–0.1 T from a $\sim$200 kg array.

Math (ideal cylinder, inner radius $r_i$, outer radius $r_o$, remanence $B_r$):

$B_{\mathrm{inside}}=B_r\ln \left(\frac{r_o}{r_i}\right)$

For $B_r=1.4\mathrm{T}$ (N52 NdFeB), $r_o/r_i=1.07$, $B_{\mathrm{inside}}=1.4\cdot 0.0677=95\mathrm{mT}$. To reach 0.5 T inside, $r_o/r_i\approx 1.42$ — a thick array. Hyperfine’s 0.064 T design trades inner uniformity for outer compactness and uses 24-segment Halbach with field shimming via passive iron blocks.

7. High-field and HTS

7.1 7 T and above clinical

Siemens MAGNETOM Terra (FDA 2017) was the first FDA-cleared 7 T whole-body for clinical use; Terra.X (2022) added Gemini gradients (200/200) and 32-channel pTx. Siemens has installed $>$ 100 units worldwide by 2025; the Philips MR 7700 (2022) is the principal competitor. Clinical indications: epilepsy presurgical mapping, neurodegenerative disease neuro-imaging, pituitary microadenoma.

7.2 Research only — 9.4 T, 10.5 T, 11.7 T, 14 T

Active whole-body installations: 9.4 T at MPI Tübingen, Maastricht, University of Minnesota CMRR, 10.5 T at CMRR Minnesota, 11.7 T at NIH Bethesda (Iseult project, NeuroSpin Saclay 11.7 T whole-body installed 2022), 14 T proposed at Univ. Iowa (Iseult-style Nb${}_3$Sn). NeuroSpin’s Iseult 11.7 T magnet weighs 132 tonnes, 1.5 km of Nb${}_3$Sn wire, $\sim$$200M project cost over 17 years.

7.3 HTS REBCO magnets

YBa${}_2$Cu${}_3$O${}_{7-\delta }$ (YBCO) and Bi${}_2$Sr${}_2$CaCu${}_2$O${}_8$ (Bi-2212) coated conductors enable magnets above 15 T at reasonable cryogenic temperatures. The Bruker UltraShield 1.2 GHz NMR (28.2 T at the sample) uses a hybrid LTS + Bi-2212 + REBCO design — the highest-field commercial NMR magnet. Whole-body REBCO MRI is at the R&D phase; the technical challenge is uniformly persistent operation in REBCO coils (which have leakage in the cuprate joints and screening currents that decay the field).

7.4 Cryogen-free HTS trend

Conduction-cooled HTS magnets (running at 20 K rather than 4 K) are emerging for spectroscopy, with companies including HyperTech, JEOL, Hitachi, and Tokamak Energy supplying coils. The first cryogen-free HTS MRI scanner (low-field, 0.5 T) was demonstrated in 2024 at the Hefei Institute of Plasma Physics.

8. MR safety

8.1 Zoning

Per ACR / IEC 60601-2-33, an MR suite is zoned:

• Zone 1 — public-accessible areas with no MR hazard.
• Zone 2 — interview / changing area; controlled access.
• Zone 3 — magnet-room exterior; only screened personnel and patients past this line.
• Zone 4 — inside the magnet room. 5-gauss line is at or near the Zone 3 / 4 boundary.

A pacemaker / ICD / cochlear implant projectile or torque incident in Zone 4 has caused the documented patient deaths in MR (8–10 published cases since 1985). Screening at the Zone 3 line is mandatory.

8.2 MR-conditional implants

Modern medical implants are labelled per ASTM F2503:

• MR Safe — no metallic content, no induced current. (Plastic IV catheters.)
• MR Conditional — safe under specified $B_0$, $dB/dt$, SAR, and time conditions. (Modern pacemakers, hip implants, stents.) Each label is specific: “1.5 T or 3 T, $dB/dt\le 200$ T/s, SAR $\le$ 2 W/kg whole-body, $\le$ 4 W/kg head, scan duration $\le$ 30 min.”
• MR Unsafe — not allowed in Zone 4. (Older pacemakers, ferromagnetic aneurysm clips.)

8.3 MRgFUS — magnetic resonance guided focused ultrasound

Insightec Exablate Neuro and Exablate Prostate integrate a focused-ultrasound transducer into a 1.5 T or 3 T MRI bore for non-invasive thermal ablation of essential-tremor, prostate cancer, and emerging Parkinson’s targets. MRI provides real-time MR thermometry (proton resonance frequency shift method) during the sonication. Approved for essential tremor since 2016, Parkinson’s tremor 2018.

8.4 RF heating of conductive implants

The 1.5 / 3 / 7 T transmit B1 induces currents in metallic implants, with heating proportional to the length-to-wavelength ratio. A 30 cm long conductive lead (e.g. an old non-MR-conditional pacemaker lead) at 64 MHz approaches resonant antenna geometry and can heat by 10–30 °C in seconds — the deadly failure mode of off-label MR scans on patients with old implants. The IEC 60601-2-33 + ASTM F2182 protocols define implant heating-test methodology; modern pacemakers (Medtronic Azure XT MRI, BIOTRONIK Lumax 740, Abbott Gallant) pass MR-conditional labelling at $\le$ 2 W/kg whole-body and limited torso-imaging-time.

8.5 Spectroscopy and non-${}^1$H imaging

Beyond proton imaging, modern scanners support spectroscopy and other nuclei:

• ${}^{31}$P MRS — phosphorus metabolism, 17.2 MHz at 1 T. Heart muscle ATP/PCr ratio for cardiac viability.
• ${}^{13}$C MRI — hyperpolarised carbon-13 (DNP, dynamic nuclear polarisation; SpinTrap, GE SPINLab) for real-time pyruvate-to-lactate metabolism imaging in prostate and cardiac tumours. Polarisation factor 10${}^4$–10${}^5$ vs thermal ${}^{13}$C.
• ${}^{23}$Na MRI — sodium in tissue (~1/5000 the signal of water ${}^1$H). Cartilage and renal sodium imaging. Standard at 7 T+ with dedicated ${}^{23}$Na coils.
• ${}^{129}$Xe MRI — hyperpolarised xenon for lung-ventilation imaging (Polarean 9820, FDA-approved 2022). Used for COPD, cystic fibrosis, pulmonary embolism.
• ${}^{19}$F MRI — fluorine for perfluorocarbon contrast tracers (CelSense Cell Sense) tracking cell therapies in vivo.

Multinuclear hardware requires a separate, broad-band RF chain (typically 30–150 MHz) and dedicated coils. Premium 3 T systems (Siemens Cima.X, Philips MR 7700, GE SIGNA Architect) include multinuclear options at $\sim$$300k each.

9. Engineering pitfalls

• Quench risk during ramp. A first ramp of a new magnet must train through small instabilities — every wire-motion event causes a small quench until the magnet “settles.” Manufacturers do this in-factory; on-site re-ramps after relocation re-train. A typical large-volume 3 T factory ramp goes through 5–20 small training quenches; the customer-facing magnet then ramps to operating current in a single uninterrupted run.
• Bore inserts and gradient strength. Smaller bore = closer gradient turns = stronger gradients at the same amp-turns. A 60 cm bore 3 T can hit 80 mT/m / 200 T/m/s; a 70 cm bore 3 T is limited to 45 mT/m / 200 T/m/s without doubling amplifier power. Premium “head-only” 3 T systems (Siemens Connectom, Bruker BioSpec 3T-Connectom) drop to 50 cm bore and hit 300 mT/m for diffusion imaging.
• Cryocooler vibration coupling. A pulse-tube at 1.4 Hz vibrates the cold-mass; the field jitters at the same frequency and shows up as ghosting. Vendors decouple the cold-head from the magnet via flexible braids.
• Iron in adjacent rooms. A nearby steel beam or HVAC duct distorts B0 by 50–500 ppm. Pre-install field maps and corrective passive shim mass are part of every install.
• Electrical-room interference. Switching gear within the same building can pulse the 50/60 Hz background; Tesla MRI scanners need $\sim$1 µT-level external field stability for clean fMRI.
• Helium-vent failure. If the quench vent is blocked (e.g. ice plug in winter, vent extension flange leak), a quench can rupture the cryostat — historically the deadliest single MR failure mode. Vent inspections every 6 months are mandated.
• Gradient amplifier failure. A driver-MOSFET short can dump full bus voltage into a gradient coil, producing forces sufficient to rupture epoxy potting. Series current-limit fuses + active over-current shutdown are the standard protection.
• B1 transmit dropouts. Adipose tissue in obese patients causes 3 T body-coil transmit non-uniformity (“dielectric shading”). pTx mitigates; otherwise the radiologist gets used to interpreting through it.

9.5 MR-Linac — MRI + radiotherapy

Elekta Unity (1.5 T MRI + 7 MV linear accelerator, FDA 2018) and ViewRay MRIdian (0.35 T MRI + 6 MV linac, FDA 2017) integrate real-time MR imaging with photon-beam radiotherapy. The patient is imaged continuously during treatment; the beam is gated on the tumour position rather than the surface skin markers. Magnetic compatibility of the linear-accelerator magnetron / klystron, gantry rotation, and MLC (multi-leaf collimator) under a 1.5 T fringe is the primary engineering challenge. Unity uses a split-bore design with the linac mounted on a ring rotor around the magnet; the radiation beam passes through low-loss windows in the cryostat.

9.6 Cardiac MR — bSSFP and tagging

Cardiac imaging at 1.5 T uses balanced steady-state-free-precession (bSSFP) sequences — the bright-blood myocardial standard. Cardiac MR requires ECG-gated acquisition (synchronised to R-wave from a 4-lead patient ECG, with MR-conditional electrodes from Medrad / Bayer or Invivo). Gradient echo planar imaging (EPI) at 3 T (and especially 7 T) suffers from increased $T_2^{\ast }$ susceptibility at the heart-lung-diaphragm interface; partial-Fourier and parallel imaging (SENSE / GRAPPA / CAIPIRINHA) mitigate.

10. Standards

• IEC 60601-2-33 — the headline MRI safety standard. Defines $B_0$ exposure limits, gradient $dB/dt$ limits, SAR limits, alarm and emergency-stop requirements.
• ASTM F2503 — implant labelling (MR Safe / MR Conditional / MR Unsafe).
• ACR MRI Accreditation Program — image-quality + safety standard for clinical accreditation in the US.
• NEMA MS series (MS-1 through MS-12) — performance-measurement methods: SNR (MS-1), image uniformity (MS-3), slice thickness (MS-5), geometric accuracy (MS-2), gradient performance (MS-7).
• DICOM Supplement 49 — MR private-tag headers; the metadata layer for scan parameters.

10.1 Quench protection and emergency procedures

A clinical scanner has an emergency run-down unit (ERDU) — a big red button (and a key-locked switch) that fires the quench heaters and dumps the magnet on command. ERDU activation is reserved for life-safety emergencies: a ferrous projectile lodged against a patient, a stuck patient table that cannot be retracted, a cardiac arrest where the patient cannot be moved out before defibrillator use. Every ERDU activation is reportable to FDA and the manufacturer. Each quench costs $\sim$$50–70k including downtime; no clinic activates it lightly.

11. Worked example — homogeneity budget for a 3 T scanner

A 3 T magnet at $\gamma B_0=127.74$ MHz Larmor frequency for ${}^1$H. The clinically-acceptable B0 inhomogeneity is $\sim$1 ppm over a 40 cm-diameter spherical volume (DSV). What does that mean in absolute Hz?

• $\Delta B/B_0=10^{-6}$ → $\Delta B=3\mu \mathrm{T}$ peak-to-peak.
• $\Delta f=\gamma \Delta B=42.58MHz/T\cdot 3\mu \mathrm{T}=128\mathrm{Hz}$.

For an echo time of 30 ms, this is a 3.8 rad phase wander across the volume — survivable for spin-echo but catastrophic for echo-planar imaging (EPI) at 2 mm voxels. EPI demands $\sim$0.05 ppm over the brain, achieved by 2nd / 3rd-order active shimming on every slice. The pre-emphasis filter on the gradient amplifier also corrects time-domain field drift from gradient eddy currents to within 1 ppm.

11.2 Helium-consumption budget — sealed vs open

A historical 1.5 T magnet with 1500 L liquid helium bath and a 2 % per month boil-off rate consumes 360 L/year, costing $\sim$$1800/year at $5/L spot price. A modern 3 T magnet with zero-boil-off ZBO cryocooler captures all evaporation and re-condenses; a typical refill is required every 5–10 years and only for service. A sealed-magnet design (Philips BlueSeal 7 L charge) needs no refill ever — the helium is purchased at install and stays.

Helium supply has been intermittently constrained — the 2018–2019 “helium shortage 4.0” saw prices triple. Major sources include the US Federal Helium Reserve (Cliffside, TX — sold by 2024), Qatar (Ras Laffan), Algeria (Skikda + Arzew), Russia (Amur GPP), and Tanzania (Helium One Global). MRI consumes $\sim$30 % of global liquid-helium production; the move to sealed magnets is structurally important to long-term MRI economics.

11.3 Reconstruction backends

A modern MRI scanner produces 200–2000 MB of k-space data per scan. Reconstruction tasks:

• 2D / 3D Fourier transform — standard for Cartesian k-space.
• Non-Cartesian gridding — for spiral, radial, PROPELLER trajectories; non-uniform FFT (NUFFT) on GPU.
• Parallel imaging — SENSE (Pruessmann 1999), GRAPPA (Griswold 2002), ESPIRIT (Uecker 2014) — exploits coil-sensitivity maps to recover undersampled k-space, accelerating scans by factors of 2–8×.
• Compressed sensing — exploits sparsity in a transform domain (wavelet, finite-difference, learned) to recover from sub-Nyquist sampling. Standard in cardiac, dynamic contrast-enhanced, MR fingerprinting.
• AI / deep-learning reconstruction — GE AIR Recon DL, Siemens Deep Resolve, Philips SmartSpeed AI, Canon AiCE, United Imaging uAI. Trained on paired full-Nyquist + undersampled data; recover image quality at 2–4× the SNR of conventional reconstruction.

GPU computing in the reconstruction backend (NVIDIA A100 / H100 in 2024–2026 generation systems) has shifted scan-time bottleneck from acquisition to reconstruction in some sequences. Hyperfine Swoop relies heavily on its AI-Powered Imaging reconstruction to make 64 mT data diagnostically usable.

12. Cost summary

System class	List price (USD, 2026)
Hyperfine Swoop 0.064 T portable	$250–350k
Magnetica 0.5 T extremity	$300–500k
Siemens MAGNETOM Free.Max 0.55 T	$0.7–1.1M
Philips Ingenia Ambition 1.5 T BlueSeal	$1.2–1.7M
Canon Vantage Orian 1.5 T	$1.0–1.5M
GE Signa Architect 3 T	$1.7–2.4M
Siemens MAGNETOM Vida 3 T	$2.0–2.8M
Siemens MAGNETOM Cima.X 3 T premium	$2.8–3.4M
United Imaging uMR Jupiter 5 T	$4–6M
Siemens MAGNETOM Terra.X 7 T	$8–15M
11.7 T research whole-body	$50–200M (project cost)

Operating cost is dominated by helium ($\sim$$5/L, sealed-magnet systems remove this entirely), service contract (8–12 % of capex/year), and electricity (continuous 25–60 kW for the magnet + chiller plant).

12.1 Operating economics

The largest line items in MR operating cost:

• Capital recovery — $1.5M – $15M amortised over 8–12 years.
• Service contract — 8–12 % capex/year. Includes preventive maintenance, parts, technician visits, software upgrades.
• Electricity — 25–60 kW continuous (magnet cryocooler + gradient amp standby + chillers + console). At $0.12/kWh, $\sim$$26k–$63k/year.
• Helium refill — $1–4k/year on legacy 1.5 T; $0 on sealed-magnet systems.
• Staffing — 1.5–2.0 FTE technologist + 0.25 FTE radiologist per scanner.
• Reading — radiologist read fees (capped by CMS schedule in US Medicare; commercial payors negotiated).

Throughput on a busy clinical 3 T is 25–40 scans/day; gross professional + technical revenue of $25k–$60k/day. ROI break-even on a new 3 T is typically 30–60 months.

13. Open-source MRI projects

A handful of open hardware and open software MRI projects have emerged since 2015:

• OCRA / Open Source Imaging Initiative (OSI${}^2$) — open-source 0.05 T MRI console electronics + magnet plans, originating at MIT and Charité Berlin.
• MaRCoS (Magnetic Resonance Console for OSI${}^2$) — open RF + gradient digital backplane.
• Pulseq (Karlsruhe + Stanford) — vendor-neutral pulse sequence description and converter to Siemens, GE, Philips, Bruker. Standard for academic sequence development.
• GIRF — Gradient Impulse Response Function library (ETH Zurich) — measure-and-pre-emphasis tooling for arbitrary gradient waveforms.
• BART (Berkeley Advanced Reconstruction Toolbox) — open-source reconstruction backend for parallel imaging, compressed sensing, ESPIRIT.
• Gadgetron (Hansen lab, NIH/NHLBI) — production-grade reconstruction streaming framework.

These projects substantially lower the barrier to research at low-field and to novel sequences on academic vendors.

Further reading

• Bernstein, M. A., King, K. F., & Zhou, X. J. (2004). Handbook of MRI Pulse Sequences. Academic Press. The canonical reference for sequence design, with detailed gradient and RF coil math.
• Vlaardingerbroek, M. T. & den Boer, J. A. (2003). Magnetic Resonance Imaging: Theory and Practice (3rd ed.). Springer. The Philips-aligned engineering textbook; clean treatment of B0 magnet, gradient, RF design.
• Roemer, P. B. et al. (1990). “The NMR phased array.” Magn. Reson. Med. 16(2): 192–225. The foundational paper for multi-channel receive arrays.
• Lvovsky, Y., Stautner, E. W. & Zhang, T. (2013). “Novel technologies and configurations of superconducting magnets for MRI.” Supercond. Sci. Technol. 26, 093001. Survey of NbTi and Nb${}_3$Sn conductor + active-shielding designs.
• Wilson, M. N. (1983). Superconducting Magnets. Oxford University Press. Reference for the underlying physics of stability, training, and quench protection — still the standard text.
• Iwasa, Y. (2009). Case Studies in Superconducting Magnets (2nd ed.). Springer. MIT-style case studies including NMR, MRI, and accelerator magnets.
• Vaughan, J. T. & Griffiths, J. R. (Eds.). (2012). RF Coils for MRI. Wiley.
• Saekho, S. et al. (2006). “Fast-kz three-dimensional tailored radiofrequency pulse for reduced B1 inhomogeneity.” Magn. Reson. Med. 55(4): 719–724. The pTx foundation.
• Glover, G. H. & Schneider, E. (1991). “Three-point Dixon technique for true water/fat decomposition with B0 inhomogeneity correction.” Magn. Reson. Med. 18(2): 371–383. Shim correction in practice.
• Sarracanie, M. et al. (2015). “Low-cost high-performance MRI.” Sci. Rep. 5, 15177. Hyperfine roots in the Wald lab at MGH.

Adjacent

• electromagnetics-engineering — Maxwell, magnetic-circuit reluctance, Faraday’s law — the foundations under every magnet, gradient, and RF coil.
• magnetic-sensors-deep — fluxgate field mapping for shim acceptance + MR-conditional Hall switches inside the scanner room.
• bioinstrumentation — ECG / EEG complementary modalities; gating ECG during MR is its own discipline.
• photonics — fiber-optic patient-monitoring leads to avoid RF coupling into the bore.
• power-electronics — gradient amplifier (IGBT / SiC H-bridge at 2 kV / 1 kA peak) and RF power amplifier (LDMOS at 35 kW peak).
• rf-design — birdcage coil resonance, transmission-line matching, LNA design at 64–300 MHz.
• quantum-materials-and-topological-phases — NbTi, Nb${}_3$Sn, REBCO superconductor microstructure and pinning.
• magnetic-and-optical-materials — soft iron yokes for passive shimming, NdFeB for permanent-magnet low-field MRI.