Surface of detonation nanodiamonds was functionalized for the covalent attachment of immunoglobulin, and simultaneously bovine serum albumin and Rabbit Anti-Mouse Antibody. The nanodiamond-IgGI125 and RAM-nanodiamond-BSAI125 complexes are stable in blood serum and the immobilized proteins retain their biological activity. It was shown that the RAM-nanodiamond-BSAI125 complex is able to bind to the target antigen immobilized on the Sepharose 6B matrix through antibody–antigen interaction. The idea can be extended to use nanodiamonds as carriers for delivery of bioactive substances (i.e., drugs) to various targets in vivo.

In the optics of charged particle beams, circular transverse modes can be introduced; they provide an adequate basis for rotation-invariant transformations. A group of these transformations is shown to be identical to a group of the canonical angular momentum preserving mappings. These mappings and the circular modes are parametrized similar to the Courant-Snyder forms for the conventional uncoupled, or planar, case. The planar-to-circular and reverse transformers (beam adapters) are introduced in terms of the circular and planar modes; their implementation on the basis of skew quadrupole blocks is described. Various kinds of matching for beams, adapters and solenoids are considered. Applications of the planar-to-circular, circular-to-planar and circular-to-circular transformers are discussed. A range of applications includes round beams at the interaction region of circular colliders, flat beams for linear colliders, relativistic electron cooling, and ionization cooling.

The head-tail modes are described for the space charge tune shift significantly exceeding the synchrotron tune. A general equation for the modes is derived. The spatial shapes of the modes, their frequencies, and coherent growth rates are explored. The Landau damping rates are also found. The suppression of the transverse mode coupling instability by the space charge is explained.

Modern and future particle accelerators employ increasingly higher intensity and brighter beams of charged particles and become operationally limited by coherent beam instabilities. Usual methods to control the instabilities, such as octupole magnets, beam feedback dampers, and use of chromatic effects, become less effective and insufficient. We show that, in contrast, Lorentz forces of a low-energy, magnetically stabilized electron beam, or “electron lens,” easily introduce transverse nonlinear focusing sufficient for Landau damping of transverse beam instabilities in accelerators. It is also important to note that, unlike other nonlinear elements, the electron lens provides the frequency spread mainly at the beam core, thus allowing much higher frequency spread without lifetime degradation. For the parameters of the Future Circular Collider, a single conventional electron lens a few meters long would provide stabilization superior to tens of thousands of superconducting octupole magnets.

Nested head-tail is a Vlasov solver for transverse oscillations in multibunch beams. It takes into account azimuthal, radial, coupled-bunch, and beam-beam degrees of freedom affected by arbitrary dipole wakes, feedback damper,beam-beam effects and Landau damping.