A probe that uses a coil and magnet to generate ultrasound directly in the surface of a conducting specimen. The coil's high-frequency current induces eddy currents, and the Lorentz force from the magnet's field (plus magnetostrictive forces in ferromagnets) makes the surface vibrate. Needing no couplant, EMATs inspect hot pipes and moving plates.

How much does EMAT sensitivity fall with liftoff?

The periodic field from the coil decays exponentially with distance from the specimen. For a 6 mm-period coil, round-trip loss is about 9 dB at 0.5 mm liftoff and 18 dB at 1 mm. A 3 mm period doubles those losses in dB, so finer coils demand tighter liftoff control.

What is coupled in EMAT analysis?

An electromagnetic analysis first gives eddy-current and force distributions, which are passed to an elastic-wave analysis as surface forces. Eddy currents sit in a skin layer much thinner than the wavelength, so they can usually be treated as surface tractions. Reception is the reverse: the vibrating conductor moving in the magnetic field drives currents that the coil picks up.

Electromagnetic Acoustic Transducer (EMAT) Analysis

Category: Coupled Analysis | Revised 2026-09-30

Theory: making the source in the specimen surface

Overview

🙋

I want to measure wall thickness on a 300 °C pipe during operation, but ordinary ultrasonic probes can't touch it. Would an EMAT work?

🎓

That's an EMAT's strength. Ordinary probes transmit a piezo element's vibration through a water or gel couplant. An EMAT drives high-frequency current in a coil to induce eddy currents in the specimen surface, under a magnet's field; the eddy currents feel a Lorentz force and the surface itself becomes the source. No contact or couplant needed. The trade-offs are low transduction efficiency and sensitivity to the gap between coil and surface.

Lorentz force and skin depth

$$ \mathbf{f} = \mathbf{J}_e \times \mathbf{B}_0, \qquad \delta = \frac{1}{\sqrt{\pi f \mu \sigma}} $$

$\mathbf{J}_e$ is eddy-current density, $\mathbf{B}_0$ the magnet's static field and $\delta$ the skin depth over which eddy currents flow. Currents gather within about $\delta$ of the surface, so the force arises in that thin layer. In ferromagnets magnetostrictive forces add, and efficiency depends strongly on the material's magnetic state.

Effect of liftoff

$$ B(z) \propto e^{-2\pi z / D} \quad\Rightarrow\quad \text{loss}_{pitch\text{-}catch} = 2 \times 20\log_{10} e^{-2\pi g / D} $$

$D$ is the spatial period of a meander coil or similar and $g$ the liftoff. A periodic field decays exponentially with distance relative to its period. It applies on both transmit and receive, doubling the dB loss. This is an idealised estimate for the periodic component; real coils add geometric effects.

Coffee Break Trivia

Rails and hot steel strip

Electromagnetic generation of ultrasound was known from the mid-20th century, but practical use grew from the 1970s. Needing no couplant, EMATs found work on targets that can't be touched — measuring the thickness of steel strip at hundreds of degrees just after rolling, or searching rails for flaws from moving inspection cars. Strong rare-earth magnets and low-noise amplifiers for faint signals offset the low efficiency and broadened their use.

Worked examples

Example 1: skin depth and wavelength

Material	Frequency	Skin depth	Shear wavelength	Ratio
Aluminium	2 MHz	0.060 mm	1.55 mm	0.04
Austenitic stainless	2 MHz	0.30 mm	1.55 mm	0.19
Carbon steel (μr = 100 assumed)	2 MHz	0.015 mm	1.61 mm	0.009
Austenitic stainless	0.5 MHz	0.60 mm	6.2 mm	0.10

Usually skin depth is a few to a dozen or so percent of the wavelength, so forces can be treated as surface loads. In low-conductivity stainless, however, it approaches 20% of the wavelength, and including the through-depth force distribution is more accurate. Carbon steel's permeability varies strongly with field, so its skin depth depends on the magnet conditions.

Example 2: sensitivity loss with liftoff

Liftoff	6 mm coil period	3 mm coil period
0.2 mm	−3.6 dB	−7.3 dB
0.5 mm	−9.1 dB	−18.2 dB
1.0 mm	−18.2 dB	−36.4 dB
2.0 mm	−36.4 dB	−72.8 dB

🙋

Just 1 mm of liftoff cuts the signal to an eighth. I wanted a protective layer for the hot pipe…

🎓

A protective layer's thickness becomes liftoff, so it's a trade-off with sensitivity. A longer coil period reduces liftoff sensitivity, but the period is tied to the wavelength you want to excite and can't be chosen freely. Oxide scale, roughness and pipe curvature also change the gap, so check in analysis that the signal stays above noise at the worst-case liftoff. Magnets weaken with temperature too, so plan their thermal management.

How to approach the analysis

Procedure

Solve the magnet's static field; for ferromagnetic specimens, obtain magnetisation state and permeability.
Solve eddy currents from the coil's high-frequency current, resolving the skin depth with several mesh layers.
Compute Lorentz (and magnetostrictive) forces and pass them to the elastic-wave analysis as surface loads.
Solve elastic waves for reflections from flaws and back walls, with at least 10–20 elements per wavelength.
For reception, compute coil voltage from surface vibration as the reverse process.

Coffee Break Trivia

“Same steel, different signal size”

On carbon-steel pipe of one grade, EMAT signal size can vary by more than a factor of two from place to place. In carbon steel, magnetostrictive forces rival the Lorentz force, and their size depends on residual magnetisation, stress and microstructure — especially near welds or areas magnetised earlier by magnetic-particle testing. Thickness measurement uses arrival time, so amplitude differences matter little, but estimating flaw size from signal strength must allow for this variation.

Common mistakes

Mistakes and fixes

Mistake	Effect	Fix
Coarse mesh in the skin layer	Wrong force magnitude	Several layers in δ
Using ideal liftoff	Insufficient signal in practice	Check worst-case liftoff
Ignoring magnetostriction in ferromagnets	Efficiency badly wrong	Add magnetostrictive forces
Coarse elastic-wave mesh	Distorted waveforms	10–20+ elements per wavelength
Ignoring magnet temperature effects	Sensitivity loss when hot	Evaluate field at temperature

🙋

I'd like to try elastic waves and skin depth myself.

🎓

Try the elastic wave simulator for elastic waves, the Lamb wave dispersion tool for plate waves and the skin depth calculator for skin depth. Force mechanisms are covered in Lorentz force and magnetostriction, and other transduction methods in piezoelectric analysis and electromagnetic forming.

Rate this article

Thank you for your feedback!

Helpful

More details

Report error