Sources of biomagnetism

Magnetic fields arise from many parts of the body and are produced by two distinct types of sources–ionic currents and magnetic tissues. Although most of the body is weakly diamagnetic, the magnetic tissues of greatest interest are paramagnetic or ferromagnetic. The major source of paramagnetism in the body is the liver, which contains iron compounds [1]. The strongest sources of ferromagnetism in the body are ingested or inhaled ferromagnetic substances, which can be detected even in trace amounts [2].

Like other electrical currents, ionic currents generated by nerve and muscle tissue produce magnetic fields and potential differences, which can be detected at the body surface or even outside the body. The ionic current has two components – a “primary” current and a “volume” current [3] (Fig. 16.1). Primary currents result directly from physiological activity and are confined largely within the electrically excited cells. Volume currents are passive return currents that extend far into the surrounding medium in response to the electromotive forces that drive the primary currents. Bioelectric signals are conducted to the body surface by volume currents and are the main source of electroencephalographic (EEG) and electrocardiographic (ECG) signals. Bioelectric signals are strongly influenced by the highly inhomogeneous electrical conductivity of the body. In contrast, biomagnetic signals arise predominantly from primary currents and are affected to a much lesser extent. This accounts for a key advantage of biomagnetic versus bioelectric fields – their simpler signal-transmission properties – which enables a more accurate determination of source location.

Introduction

Optically pumped helium (He) magnetometers have provided magnetic field data for military, aeromagnetic survey, space exploration and geophysical laboratory applications for over five decades. The characteristics of He magnetometers that have made them instruments of choice for these varied applications include high sensitivity, high accuracy, simplicity of the resonance line, small heading errors due to light shifts, temperature independence of resonance cells, linear relationship between the magnetic field and the resonance frequency, excellent stability for gradiometer operation and robustness for field and space use. Scalar He magnetometers can easily be configured for omnidirectional operation with no moving parts to provide full sensitivity on all headings relative to the magnetic field direction.

Helium magnetometers have two types of optical pumping radiation sources. All He magnetometers manufactured from 1960 to 1990 utilized an RF electrodeless discharge He-4 lamp as an optical pumping source of 1083 nm resonance radiation which is composed of three closely spaced He-4 resonance lines D0, D1, and D2. In the 1980s, the development efforts for a single-line pump source for both He magnetometers and basic research on He isotopes resulted in both high-efficiency semiconductor lasers and optical fiber lasers at 1083 nm. Laser-pumped He magnetometers are characterized by sensitivities up to two orders of magnitude better than lamp-pumped He magnetometers and are more accurate, smaller, and very stable for use in magnetic gradiometers. L. D. Schearer provided a comprehensive review of the beginning science of He-4 magnetometers [1] and a review of the first 25 years of progress in optically pumped He magnetometers [2].

Introduction

Shortly after the inception of atomic magnetometry, alkali-vapor magnetometers were being used to measure the Earth's magnetic field to unprecedented precision. During the same era, Bell and Bloom first demonstrated all-optical atomic magnetometry through synchronous optical pumping [1] (see Chapters 1 and 6). In this approach, optical-pumping light is frequency- or amplitude-modulated at harmonics of the Larmor frequency ωL to generate a precessing spin polarization within an alkali vapor at finite magnetic field [2, 3]. Although this technique received considerable attention from the atomic physics community for its applicability to optical pumping experiments, Earth's-field alkali-vapor atomic magnetometers continued to rely on radiofrequency (RF) field excitation for several decades (see Chapter 4). Upon the advent of diode lasers addressing alkali and metastable helium transitions, synchronously pumped magnetometers experienced a revival beginning in the late 1980s. In recent years, such magnetometers have found applications in nuclear magnetic resonance detection [4] (see also Chapter 14), quantum control experiments [5], and chip-scale devices intended for spacecraft use [6] (see also Chapters 7 and 15).

All-optical magnetometers possess several advantages over devices that employ RF coils. RF-driven magnetometers can suffer from cross-talk if two sensors are placed in close proximity, since the AC magnetic field driving resonance in one vapor cell can adversely affect the other. All-optical magnetometers are free from such interference. When operated in self-oscillating mode [7], RF-driven magnetometers require an added ±90° electronic phase shift in the feedback loop to counter the intrinsic phase shift between the RF field and the probe-beam modulation.

Introduction

Applications such as geophysical exploration for minerals and oil, anti-submarine warfare, volcanology, earthquake studies, magnetic observatories, and the detection of buried objects at sites of archaeological significance require instruments that can measure small variations of the Earth's magnetic field in time and space. Other applications such as laboratory metrology, space exploration, and biomedicine may require measurements at lower or higher fields. The demand for precise measurements of magnetic fields is met in part by commercial atomic magnetometers supplied by a number of manufacturers over the last fifty years. Commercial optical magnetometers based on cesium, potassium, and helium are now firmly established. Commercial magnetometers designed for measuring anomalies in the Earth's field are typically operated as self-oscillating devices or VCO (voltage-controlled oscillator) lock-in devices with the oscillation or lock-in frequency proportional to the magnetic field. This chapter examines the specifications for atomic magnetometers, compares the most widely used approaches, describes some of the features demanded by different applications, and surveys the history of atomic magnetometers. (The online supplemental material contains a table listing many of the United States patents related to the field of atomic magnetometry.)

Earth's field at the surface ranges from 20 to 80 μT. Typically the user is seeking to generate a map of the local magnetic field upon which magnetic anomalies can be discerned. The map may be made by means of a walking survey, for instance in the case of archaeological sites. For mineral exploration much wider areas must be surveyed, so that typically airborne and ground surveys are required. The magnetic anomalies can be in the pT range or even smaller. For such applications, the most significant requirement for the magnetometer is its sensitivity.

Introduction

While atomic magnetometers can measure magnetic fields with exceptional sensitivity and without cryogenics, spin-altering collisions limit the sensitivity of sub-millimeter-scale sensors [1]. In order to probe magnetic fields with nanometer spatial resolution, magnetic measurements using superconducting quantum interference devices (SQUIDs) [2–4] as well as magnetic resonance force microscopes (MRFMs) [5–8] have been performed. However, the spatial resolution of the best SQUID sensors is still not better than a few hundred nanometers [9] and both sensors require cryogenic cooling to achieve high sensitivity, which limits the range of possible applications. A related challenge that cannot be met with existing technology is imaging weak magnetic fields over a wide field of view (millimeter scale and beyond) combined with sub-micron resolution and proximity to the signal source under ambient conditions.

Recently, a new technique has emerged for measuring magnetic fields at the nanometer scale, as well as for wide-field-of-view magnetic field imaging, based on optical detection of electron spin resonances of nitrogen-vacancy (NV) centers in diamond [10–12]. This system offers the possibility to detect magnetic fields with an unprecedented combination of spatial resolution and magnetic sensitivity [8, 12–15] in a wide range of temperatures (from 0 K to well above 300 K), opening up new frontiers in biological [10, 16, 17] and condensed-matter [10, 18, 19] research. Over the last few years, researchers have developed techniques for nanoscale magnetic imaging in bulk diamond [11, 12, 20] and in nanodiamonds [21–23] along with scanning probe techniques [10, 24].

Introduction

Soon after the development of optical magnetometers based on the radio-optical double resonance method (see Chapter 4), it was realized by Bell and Bloom [1] that an alternative method for optical magnetometry was to modulate the light used for optical pumping at a frequency resonant with the Larmor precession of atomic spins. In a Bell-Bloom optical magnetometer, circularly polarized light resonant with an atomic transition propagates through an atomic vapor along a direction transverse to a magnetic field B. Atomic spins immersed in B precess at the Larmor frequency ΩL, and when the light intensity is modulated at Ωm = ΩL, a resonance in the transmitted light intensity is observed. The essential ideas of the Bell–Bloom optical magnetometer are reviewed in Chapter 1 (Section 1.2), and can be summarized in terms of what Bell and Bloom termed optically driven spin precession: in analogy with a driven harmonic oscillator, in a magnetic field B atomic spins precess at a natural frequency equal to ΩL and the light acts as a driving force oscillating at the modulation frequency Ωm. From another point of view, the Bell-Bloom optical magnetometer can be described in terms of synchronous optical pumping: when Ωm = ΩL, there is a “stroboscopic” resonance in which atoms are optically pumped into a spin state stationary in the frame rotating with ΩL. Depending on the details of the atomic structure, the spin state stationary in the rotating frame can be either a dark state that does not interact with the modulated light or a bright state for which the strength of the light–atom interaction is increased.

(e,2e) processes – an overview

An (e,2e) process is one where an electron, of well-defined energy and momentum, is fired at a target, ionizes it and the two exiting electrons are detected in coincidence. The energies and positions in space of these electrons are determined by the experiment, so in effect all but the spin quantum numbers are then known. We can, therefore, describe it as a kinematically complete experiment; if we could also measure all the spins we would have all the information from a scattering experiment that quantum mechanics will allow. The technique offers both the possibility of a direct determination of the target wave function and a profound insights into the nature of few-body interactions. What information you extract from such an experiment really depends on the kinematics you chose and the target you use. Integrated cross sections can be crude things and you need the full power of a highly differential measurement to tease out the delicacies of the interactions. Indeed, often the most intriguing effects turn up in peculiar geometries where the cross sections are small and where a number of relatively subtle few-body interactions are present.

In recent years, attempts to give a complete numerical treatment of electron impact ionization have made considerable progress. In particular, one should mention the pioneering close coupling work of Curran and Walters [1–3], the convergent close coupling approach, [4], the complex exterior scaling calculations, [5], and the propagating exterior complex scaling method, [6].

Introduction

The accurate solution of the Schrödinger equation (SE) for electron-impact collisions leading to discrete elastic and inelastic scattering progressed rapidly with the increase in computing power from the 1970s. A review of the principal methods, including second Born, distorted wave, R-matrix, intermediate-energy R-matrix, pseudo-state close coupling and optical model is given in [1]. However, electron impact collisions leading to ionization on even the simplest atom, hydrogen, were by comparison poorly described; significant progress dates only from the early 1990s when Bray and Stelbovics [2] developed a technique called convergent close coupling (CCC). In this approach they used an in-principle complete set of functions to approximate the hydrogenic target states, both bound and continuous, and used the coupled channels formalism to expand the scattering wave function in these discretized states, reducing the solution of the SE to a set of coupled linear equations in a single co-ordinate. The method was tested in a non-trivial model [3] and shown to provide convergent cross sections not only for discrete elastic and inelastic processes but also for the total ionization cross section. Shortly thereafter the method was applied to the full collision problem from atomic hydrogen and one of the major achievements of the method was that it yielded essentially complete agreement with the (then) recent experiment for total ionization cross section [4]. In the following years, the method was applied to other atoms with considerable success; the range of applications of CCC are covered in the review of Bray et al. [5].

Introduction

The (e,2e) process for an atom describes an electron-impact-induced ionization event in which the momentum states of the incident and two outgoing electrons are defined, i.e., the reaction kinematics is fully specified. Due to its highly differential nature, the cross section describing this process provides a stringent test of electron-scattering theory. However, a quantum mechanically complete description of the (e,2e) process requires additional variables to be specified, namely the spin projection states of the continuum electrons, as well as angular momentum, and its projection state for the target atom before and the residual ion after the collision, respectively. While the goal of performing such a complete measurement is presently beyond experimental capabilities, (e,2e) experiments for which a subset of the quantum mechanical variables were determined have been performed. All employed beams of polarized electrons, enabling cross sections to be determined individually for the two spin states of the projectile (namely ms = ±½); others additionally resolved the angular momentum state of the target atom prior to the collision. In this chapter we will illustrate how the resolution of angular momentum states can powerfully highlight and provide new insight into specific aspects of the (e,2e) collision dynamics.

Electron spin emerges naturally from the relativistic treatment of quantum mechanics and, as a consequence, spin-resolved experiments are ideally suited to probe aspects of relativity in electron–atom scattering. Less obvious is that in the non-relativistic limit, spin-resolved measurements provide a sensitive probe to the nature of electron exchange processes in the (e,2e) ionization dynamics.

Introduction

Electron–electron correlation plays a crucial role in determining physical and chemical properties in a wide class of materials that exhibit fascinating properties including, for example, high-temperature superconductivity, colossal magnetoresistance, metal insulator or ferromagnetic anti-ferromagnetic phase transitions, self assembly and quantum size effects. Furthermore, electron–electron correlation governs the dynamics of charged bodies via long-range Coulomb interaction, whose proper description constitutes one of the more severe tests of quantum mechanics.

Nevertheless, the effects due to correlation remain rather elusive for almost all of the experimental methods currently used to investigate matter in its various states of aggregation. Indeed, being related to processes with two active electrons, like satellite structures in photoemission (i.e., ionization processes with one ejected and one excited electron), or double ionization events, they influence marginally the spectral responses of the target, that are primarily determined by single and independent particle behaviours. Hence the experimental effort devoted in the last 30 years to develop a new class of experiments, whose spectral response is determined mainly by the correlated behaviour of electron pairs.

The common denominator of this class of experiments is the study of reactions whose final state has two holes in the valence orbitals and two unbound electrons in the continuum. It is exactly through interaction of these holes and electron pairs that correlation shapes the cross section of the double ionization processes.