This paper focuses on the near-field beam tracking problem in high-frequency wireless communication systems using dynamic metasurface antennas (DMAs). The authors propose a near-field beam tracking framework that initiates beam sweeping only when the base station (BS) estimates that its beamforming gain drops below a threshold from its optimal value. They derive novel analytical expressions for the correlation function between beam focusing vectors, the beamforming gain under user coordinate mismatches, the direction of the user movement that yields the fastest beamforming gain deterioration, and the minimum user displacement for a certain performance loss. A non-uniform coordinate grid is designed to effectively sample the user area of interest at each position estimation slot. The proposed framework is validated through extensive simulations, demonstrating its superiority over benchmarks. The key contributions include: 1. **Analytical Expressions**: Novel expressions for the correlation function, beamforming gain under user coordinate mismatches, and the direction of the fastest beamforming gain deterioration. 2. **Non-Uniform Coordinate Grid**: A dynamic non-uniform coordinate grid for efficient sampling of the user area of interest. 3. **Near-Field Beam Tracking Framework**: A framework that initiates beam sweeping based on the estimated beamforming gain and the effective beam coherence time. The paper also discusses the system and channel models, beamforming optimization for a given UE position, and the effective beam coherence time metric. The proposed framework is designed to improve the efficiency and performance of near-field beam tracking in high-frequency wireless communication systems.This paper focuses on the near-field beam tracking problem in high-frequency wireless communication systems using dynamic metasurface antennas (DMAs). The authors propose a near-field beam tracking framework that initiates beam sweeping only when the base station (BS) estimates that its beamforming gain drops below a threshold from its optimal value. They derive novel analytical expressions for the correlation function between beam focusing vectors, the beamforming gain under user coordinate mismatches, the direction of the user movement that yields the fastest beamforming gain deterioration, and the minimum user displacement for a certain performance loss. A non-uniform coordinate grid is designed to effectively sample the user area of interest at each position estimation slot. The proposed framework is validated through extensive simulations, demonstrating its superiority over benchmarks. The key contributions include: 1. **Analytical Expressions**: Novel expressions for the correlation function, beamforming gain under user coordinate mismatches, and the direction of the fastest beamforming gain deterioration. 2. **Non-Uniform Coordinate Grid**: A dynamic non-uniform coordinate grid for efficient sampling of the user area of interest. 3. **Near-Field Beam Tracking Framework**: A framework that initiates beam sweeping based on the estimated beamforming gain and the effective beam coherence time. The paper also discusses the system and channel models, beamforming optimization for a given UE position, and the effective beam coherence time metric. The proposed framework is designed to improve the efficiency and performance of near-field beam tracking in high-frequency wireless communication systems.