This project provides a comprehensive analytical review of the Karlsruhe Tritium Neutrino (KATRIN) experiment, exploring its theoretical underpinnings, complex instrumentation, and latest empirical findings. Conducted as a term paper for the "Detector & Accelerator Technology" course at NTUA, the report examines the technical challenges of measuring the absolute mass scale of neutrinos using model-independent kinematics.

The theoretical analysis and hardware evaluation developed in this study cover:

• Neutrino Kinematics & $\beta$-Decay: Mathematical formulation of neutrino flavor oscillations (PMNS matrix) and the precise modeling of molecular tritium ($\mathrm{T_2}$) $\beta$-decay. The analysis focuses on the differential decay rate near the 18.6 keV endpoint energy, incorporating complex theoretical corrections (e.g., final-state distributions, radiative corrections).
• Source & Transport Infrastructure: Evaluation of the Windowless Gaseous Tritium Source (WGTS) operating at 30 K via two-phase Neon cooling to maintain strict column density stability. Analysis of the $10^{14}$ tritium flow reduction achieved by the Differential Pumping Section (DPS chicane) and Cryogenic Pumping Section (CPS Argon frost).
• MAC-E Filter Spectrometry: Operational principles of Magnetic Adiabatic Collimation combined with an Electrostatic filter. The report details how this configuration acts as a high-pass integrating energy filter, achieving an unprecedented energy resolution of $\Delta E \approx 0.93$ eV.
• Background Reduction & Detection: Investigation into the mitigation of Penning traps and Rydberg atom ionizations using inner wire electrodes and a Shifted Analyzing Plane (SAP). Electrons are ultimately counted using a segmented 148-pixel silicon p-i-n diode Focal Plane Detector (FPD).
• Data Analysis & Results: Review of the statistical convolution of the experimental response function with the theoretical $\beta$-spectrum. The combined data from the KNM1 through KNM5 campaigns resulted in a world-leading upper limit for the effective neutrino mass of $m_\nu <$ 0.45 eV (90% C.L.).

Below are visual representations highlighting the experimental setup and the theoretical modulation of the tritium $\beta$-decay spectrum:

The complete academic review and the accompanying presentation slides are available below.

Note: The detailed report and presentation are written in Greek, though the embedded mathematics, schematics, and data plots follow universal scientific notation.

• The KATRIN Experiment: Direct Neutrino Mass Measurement (PDF)
• Presentation Slides: The KATRIN Experiment (PDF)

This project provides a comprehensive analytical review of the Sudbury Neutrino Observatory (SNO), detailing the experimental and detection mechanisms that definitively resolved the Solar Neutrino Problem. Conducted as a term paper for the "Detector & Accelerator Technology" course at NTUA, the report evaluates how SNO successfully measured both the total and electron-specific solar neutrino fluxes independently of the Standard Solar Model (SSM).

The theoretical analysis and hardware evaluation developed in this study cover:

• Neutrino Oscillation & the MSW Effect: Mathematical detailing of PMNS matrix flavor transformations and the Mikheyev-Smirnov-Wolfenstein (MSW) effect, which explains how electron neutrinos ($v_e$) change flavor due to elastic scattering interactions while propagating through dense solar matter.
• Heavy Water Cherenkov Detection: Evaluation of the detector infrastructure, comprising a 1000-ton ultra-pure heavy water ($\mathrm{D_2O}$) target housed in a 12m diameter acrylic vessel. The target is surrounded by 9438 inward-facing Photomultiplier Tubes (PMTs) designed to capture Cherenkov radiation from electrons exceeding the local phase velocity of light.
• Statistical Cross-Section Separation: Differentiation of the three primary neutrino reaction channels: Charged-Current (CC) for exclusive $v_e$ measurement, Neutral-Current (NC) for flavor-independent total flux measurement, and Elastic Scattering (ES) for highly directional solar tracking.
• Experimental Phasing Strategies: Analysis of the observatory's three operational phases, which sequentially utilized pure $\mathrm{D_2O}$, the addition of ultra-pure $\mathrm{NaCl}$ to enhance neutron capture for the NC reaction, and the deployment of $\mathrm{^3He}$ proportional counters (NCDs) for distinct NC event tracking.
• Resolution of the Solar Neutrino Problem: Review of the empirical data demonstrating that the total solar neutrino flux (derived from NC events) matches the predictions of the SSM, while the CC/NC ratio of approximately 30% definitively proved $v_e$ flavor transformation.

Below are visual representations highlighting the experimental setup and the resulting neutrino flux measurements:

The complete academic review is available below.

Note: The detailed report is written in Greek, though the embedded mathematics, schematics, and data plots follow universal scientific notation.

• The Sudbury Neutrino Observatory (PDF)

This project provides a comprehensive theoretical foundation and analytical resolution of the Bateman equations, which govern the time evolution of nuclide concentrations in radioactive decay chains. Conducted as a bibliographic term paper for the "Nuclear Physics & Applications" course at NTUA, the report bridges classical analytical derivations with modern computational algorithms used to solve extensive nuclear decay networks.

The theoretical analysis and algorithmic evaluations developed in this study cover:

• Analytical Solutions: Derivation of the Bateman equations as a system of coupled first-order linear differential equations. The report presents rigorous analytical solutions using both inductive mathematical proofs and Laplace transforms to determine nuclide populations over time.
• Equilibrium States: Analysis of specific limiting cases in decay chains, mathematically modeling transient and secular (permanent) equilibrium states based on the relative magnitudes of the constituent decay constants ($\lambda$).
• Numerical & Algorithmic Methods: Evaluation of computational challenges in solving Bateman equations for complex networks, particularly addressing catastrophic cancellation caused by nearly identical decay constants ($\lambda_i \approx \lambda_j$) in denominators. The study reviews robust algorithmic alternatives—including matrix exponentials (eigenvalue methods), Cauchy products, and divided differences (Cetnar's solution)—and notes their implementation in industry-standard simulation software like ORIGEN, MCNP6, and Geant4.
• Modern Applications: Exploration of the practical utility of Bateman equations across critical fields. Applications detailed include Nuclear Medicine (optimizing Mo-99/Tc-99m generators for SPECT imaging), Nuclear Reactor Fuel Cycles (managing Xe-135 neutron poisoning), radiometric dating (Pb-U, Pb-Th), and radioactive waste management.

The complete academic review and the accompanying presentation slides are available below.

Note: The detailed report and presentation are written in Greek, though the embedded mathematics, schematics, and data plots follow universal scientific notation.

• Bateman Equations in Radioactive Series: Report (PDF)
• Bateman Equations in Radioactive Series: Presentation (PDF)

This project explores the non-linear dynamics of a charged particle interacting with counter-propagating electrostatic waves. Developed for the "Introduction to the Science & Technology of Controlled Thermonuclear Fusion" course, this analysis bridges fundamental Hamiltonian mechanics with advanced chaos theory.

The analytical and computational models developed in this study cover:

• Hamiltonian Mechanics & Phase Space: Formulation of the unperturbed single-wave system as a non-linear pendulum. Identification of stable and unstable fixed points, mathematical derivation of the separatrix width, and classification of librational and rotational orbits.
• Canonical Perturbation Theory: Introduction of the second, weaker electrostatic wave as a time-dependent perturbation. Transformation into action-angle variables and application of the KAM (Kolmogorov-Arnold-Moser) theorem to analyze resonance behavior.
• Chaos Theory & Stroboscopic Mapping: Implementation of stroboscopic Poincaré sections using Python to track orbital trajectories over time.
• Transition to Global Chaos: Visualizing the breakdown of KAM tori into resonance islands, the onset of chaotic scattering near the separatrix, and the eventual transition to global chaos evaluated via the Chirikov resonance overlap criterion.

Below are visual representations of the phase space contours for the unperturbed system, alongside a Poincaré section demonstrating the onset of chaos in the perturbed state:

The complete Python scripts used for the numerical integration and plotting are hosted on my GitHub Repository and are also appended to the final assignment. The detailed mathematical proofs, theoretical frameworks, and extended phase space maps are available in the original coursework assignment below.

Note: The detailed assignment is written in Greek, though the embedded mathematics, Python source code, and data plots follow universal scientific notation.

• Wave-Particle Interaction & Chaos Analysis (PDF)

This collection comprises extensive solutions and MATLAB implementations for the Computational Fluid Dynamics (CFD) coursework at NTUA. The project demonstrates a systematic progression from fundamental numerical linear algebra to the simulation of transient and multi-dimensional fluid flows.

The computational models and scripts developed throughout these problem sets cover:

• Linear System Solvers: Implementation of the Thomas Algorithm for tridiagonal systems, alongside Jacobi, Gauss-Seidel, and Successive Over-Relaxation (SOR) methods.
• Initial Value Problems: Error analysis and order-of-convergence testing for Explicit/Implicit Euler and Runge-Kutta (2nd, 3rd, and 4th order) methods.
• Boundary Value Problems: Finite difference solutions for 1D Poiseuille flow and 2D elliptic equations modeling fully-developed, steady, laminar flow in a square duct.
• Transient Diffusion: Application of Explicit, Simple Implicit, and Crank-Nicolson schemes to 1D heat diffusion, including von Neumann stability analysis.

Below are visual representations of the velocity profile and velocity contours for the fully-developed flow of an incompressible fluid through a square cross-section, solved via the Gauss-Seidel method:

The complete MATLAB scripts are hosted on my GitHub Repository, and are also incorporated in the solutions. The detailed mathematical proofs, numerical analysis, and error plots are available in the original coursework solutions below.

Note: The detailed solutions are written in Greek, though the embedded mathematics, MATLAB source code, and data plots follow universal scientific notation.

• Numerical Methods for Linear Systems (PDF)
• Numerical Methods for Initial Value Problems (PDF)
• Finite Difference Method: Poiseuille Flow (PDF)
• Finite Difference Method: Elliptic B.V.P. (PDF)
• Diffusion Equation: 1D Transient Solutions (PDF)

This report details the experimental procedure and computational data analysis for measuring the spontaneous decay lifetime of cosmic-ray muons. The experiment was conducted as part of the "Nuclear Physics & Elementary Particles Laboratory" coursework at NTUA.

The physical analysis and data processing methods developed in this report cover:

• Particle Detection: Operation of a plastic scintillator coupled with a photomultiplier tube (PMT) to capture the ionization and subsequent photon emission caused by incoming muons.
• Signal Processing: Use of a two-stage amplifier, a discriminator with adjustable voltage thresholds for noise reduction, and an FPGA timing circuit to record the time interval between a muon's entry and its decay.
• Statistical Data Fitting: Processing raw timing data using Python to generate decay histograms. The mean lifetime was extracted through least-squares exponential fitting, incorporating background signal modeling.
• Theoretical Implications: Calculation of the Fermi coupling constant ($G_F$) from the experimentally determined mean lifetime, reflecting the strength of the weak interaction. Furthermore, the survival of atmospheric muons to sea level is analyzed as a direct verification of relativistic time dilation and length contraction.

The extensive laboratory method and data analysis is available in the original report below.

Note: The detailed laboratory report is written in Greek, though the embedded mathematics, Python source code, and data plots follow universal scientific notation.

• Measurement of the Muon Lifetime (PDF)

This report details the experimental investigation of Compton scattering and the interaction of gamma rays with matter. Conducted as part of the "Nuclear Physics & Elementary Particles Laboratory" coursework at NTUA, the experiment leverages scintillation detectors to construct and analyze energy spectra from various radioactive sources.

The physical phenomena and experimental methodologies explored in this report cover:

• Gamma Ray Interactions: Theoretical and experimental analysis of the three primary interaction mechanisms within a NaI(Tl) scintillator: the Photoelectric effect, Compton scattering, and Pair production.
• Spectrum Construction: Operation of a Photomultiplier Tube (PMT) and a Multi-Channel Analyzer (MCA) to record and shape pulse-height diagrams. Analysis of the resulting spectra to identify characteristic features, including the photopeak, Compton edge, and backscatter peak.
• Electron Rest Mass Determination: Utilizing the measured energies of the photopeak, Compton edge, and backscatter peak from $\mathrm{{}^{22}Na}$, $\mathrm{{}^{60}Co}$, and $\mathrm{{}^{137}Cs}$ sources to experimentally calculate the electron rest mass ($m_e c^2$).
• Relativistic Kinematics: Calculation of the maximum kinetic and total relativistic energy of the scattered electrons. The results are compared against classical mechanics predictions, clearly demonstrating the relativistic mass-energy equivalence at speeds approaching the speed of light ($v_{max} \approx 0.92c$).

Note: The detailed laboratory report is written in Greek, though the embedded mathematics, data tables, and plots follow universal scientific notation.

• Compton Scattering Analysis (PDF)

This report explores the implementation and statistical properties of various basic Monte Carlo algorithms. Conducted as part of the "Nuclear Physics & Elementary Particles Laboratory" coursework at NTUA, the study demonstrates how pseudo-random sampling can be leveraged for numerical integration and the simulation of stochastic physical processes.

The computational analysis and numerical methods developed in this study cover:

• Pseudo-Random Number Generation: Statistical evaluation of sequences following uniform and Gaussian distributions using Octave. Analysis of how the ratio of generated numbers to histogram bins affects the precision and visual resolution of the simulated distributions.
• Numerical Integration (Calculation of $\pi$): Comparison of three distinct Monte Carlo integration techniques. The initial geometric "hit-or-miss" approach was refined into a functional Riemann sum estimation, and finally optimized using a change of variables (importance sampling) with a specific weight function. The importance sampling method successfully estimated $\pi$ to five significant figures.
• Simulation of Radioactive Decay: Modeling the exponential decay of a free neutron population ($\tau = 886.7$ s). A stochastic algorithm was implemented to simulate individual particle decay based on calculated probability distributions. The simulated data was fitted with an exponential decay curve, yielding results in excellent agreement with the theoretical mean lifetime.

The extensive laboratory method and data analysis is available in the original report below.

Note: The detailed laboratory report is written in Greek, though the embedded mathematics, Octave source code, and data plots follow universal scientific notation.

• The Monte Carlo Method (PDF)

This report investigates the phenomenon of Nuclear Magnetic Resonance (NMR) by measuring the magnetic susceptibility and resonant behavior of hydrogen protons in glycerin. Conducted as part of the "Atomic & Molecular Physics Laboratory" coursework at NTUA, the experiment bridged classical electrodynamics with quantum mechanical models of nuclear spin.

The physical phenomena and experimental methodologies explored in this report cover:

• Theoretical Framework: Comprehensive analysis of NMR using both classical Larmor precession models and quantum mechanical Zeeman energy splitting ($E = \pm \frac{1}{2}g_N \beta_N B_0$) for spin-1/2 particles.
• Signal Detection & Bloch Equations: Utilization of an AC bridge circuit and an oscilloscope to capture the NMR signal. The resonance condition was identified via the zero-crossing of the real part of the complex magnetic susceptibility ($\chi'$), adhering strictly to Bloch's equations.
• Magnetic Resonance Saturation: Qualitative observation and theoretical explanation of the saturation effect. It was demonstrated that as the amplitude of the transverse RF magnetic field ($B_x$) increases, the population difference between energy states diminishes, causing a corresponding drop in the NMR signal intensity.
• Nuclear Landé g-factor Determination: Experimental calculation of the proton Landé g-factor ($g_N$) by mapping the linear relationship between the applied static magnetic field ($B_0$) and the resonant RF frequency ($f_0$). The resulting value ($g_N = 5.61 \pm 0.15$) aligned closely with the theoretical constant ($5.5857$).

Note: The detailed laboratory report is written in Greek, though the embedded mathematics, data tables, and plots follow universal scientific notation.

• Nuclear Magnetic Resonance Analysis (PDF)

This report examines the linear emission spectrum of the Sodium ($\mathrm{Na}$) atom, focusing on the fine structure splitting of its characteristic yellow D-lines. Conducted as part of the "Atomic & Molecular Physics Laboratory" coursework at NTUA, the experiment utilizes optical spectroscopy to measure atomic emission wavelengths and quantify quantum mechanical spin-orbit interactions.

The theoretical analysis and optical measurements developed in this study cover:

• Optical Spectroscopy: Use of a reflection grating spectrometer equipped with a high-density optical grating ($N = 1800$ lines/mm) to resolve the visible emission spectrum of a Sodium vapor lamp.
• Wavelength Determination: Experimental measurement of the diffraction angles to calculate the wavelengths of the red, yellow-green, and yellow spectral lines.
• Spin-Orbit Coupling (L-S Coupling): Theoretical modeling of the Sodium D-line doublet ($\mathrm{D_1}$ and $\mathrm{D_2}$), caused by the internal magnetic interaction between the valence electron's spin and its orbital angular momentum during $3^2P_{1/2} \rightarrow 3^2S_{1/2}$ and $3^2P_{3/2} \rightarrow 3^2S_{1/2}$ transitions.
• Energy Splitting Calculation: Empirical calculation of the fine structure energy splitting ($\Delta E_{D_1,D_2}$) derived directly from the resolved doublet wavelengths. The report also explores the theoretical limits and resolving boundaries of the reflection grating for higher-order diffraction fringes.

Note: The detailed laboratory report is written in Greek, though the embedded mathematics, data tables, and plots follow universal scientific notation.

• Fine Structure of the Sodium Atom (PDF)

This report investigates the quantization of atomic energy levels through the Franck-Hertz experiment, utilizing a Neon (Ne) gas tube. Conducted as part of the "Atomic & Molecular Physics Laboratory" coursework at NTUA, the experiment provides direct empirical evidence for the Bohr model by tracking the energy losses of free electrons undergoing inelastic collisions with Neon atoms.

The physical phenomena and experimental methodologies explored in this report cover:

• Thermionic Emission & Contact Potential: Production of free electrons via a heated $\mathrm{LaB_6}$ cathode. The external contact potential difference between the $\mathrm{LaB_6}$ cathode and the Nickel ($\mathrm{Ni}$) anode was experimentally determined through current-voltage curve shifts ($U_{\epsilon\pi} = 1.6 \pm 0.5$ V).
• Inelastic Collisions & Energy Quantization: Measurement of the electron current ($I_3$) reaching the collection plate as a function of the accelerating voltage ($U_2$). The resulting periodic current drops successfully confirmed the hypothesis that electrons lose their entire kinetic energy upon inelastic collisions.
• First Excitation Energy: Experimental determination of Neon's first excitation energy ($E_1 = 17.7 \pm 1.3$ eV) by mapping the voltage intervals between consecutive current minima.
• Visible Emission Spectra: Observation of discrete red luminous fringes within the primary acceleration chamber, corresponding to the $3p \rightarrow 3s$ (or $E_2 \rightarrow E_1$) atomic de-excitations.

Note: The detailed laboratory report is written in Greek, though the embedded mathematics, data tables, and plots follow universal scientific notation.

• The Franck-Hertz Experiment (PDF)

This report investigates the phenomenon of Electron Paramagnetic Resonance (EPR) by observing the resonant behavior of the unpaired electron in the DPPH organic radical. Conducted as part of the "Condensed Matter Physics" laboratory coursework at NTUA, the experiment bridges classical electrodynamics with quantum mechanical models of electron spin and magnetic susceptibility.

The physical phenomena and experimental methodologies explored in this report cover:

• Theoretical Framework: Comprehensive analysis of EPR using both classical Larmor precession models ($\Omega_L = \gamma_e B_0$) and the quantum mechanical formulation of Zeeman energy splitting ($\Delta E = g_S \mu_B B_0$) for spin-1/2 particles.
• Signal Detection & Bloch Equations: Utilization of an AC bridge circuit, a 146 MHz RF generator, and Helmholtz coils with 50 Hz modulation to capture the EPR signal on an oscilloscope. The resonance condition was identified via the global maximum of the imaginary part of the complex magnetic susceptibility ($\chi''$), strictly adhering to Bloch's equations.
• Electron Spin g-factor Determination: Experimental calculation of the Landé g-factor for the electron spin ($g_S$) by determining the resonance static magnetic field ($B_0$). The resulting value ($g_S = 2.00 \pm 0.07$) strongly aligns with the theoretical free-electron constant ($2.00232$).
• Spin-Spin Relaxation Time: Analysis of the local magnetic field interactions between neighboring dipoles. By measuring the resonance curve's half-maximum broadening ($\Delta B_{0.5}$), the transverse spin-spin relaxation time was experimentally calculated ($T_2 = (2.4 \pm 0.6) \cdot 10^{-8}$ $\mathrm{s}$).

Note: The detailed laboratory report is written in Greek, though the embedded mathematics, data tables, and plots follow universal scientific notation.

• Electron Paramagnetic Resonance Analysis (PDF)

This laboratory report investigates the photoconductive properties of Cadmium Sulfide ($\mathrm{CdS}$) semiconductors, analyzing how electrical conductivity responds to variations in incident light intensity and photon frequency. Conducted as part of the "Condensed Matter Physics" laboratory coursework at NTUA, the experiment connects semiconductor band theory with macroscopic optical responses.

The physical phenomena and experimental methodologies explored in this report cover:

• Fundamental Absorption & Carrier Generation: Theoretical overview of photon-induced electron transitions across the direct bandgap of $\mathrm{CdS}$. Analysis of carrier generation, recombination dynamics, and the resulting equilibrium photoconductivity.
• Intensity Dependence: Measurement of photocurrent-voltage ($I_{ph}-V$) characteristics using a variable polarization setup (analyzer-polarizer) to modulate the intensity of incident white light. The results empirically verified Malus's Law and confirmed the linear relationship between steady-state photoconductivity and incident light intensity ($\sigma_{ph} \propto I$).
• Spectral Response: Prism-based spectral decomposition of the light source to measure the photocurrent as a function of incident photon energy (wavelength). Raw data was normalized against the theoretical Planck blackbody radiation spectrum to extract the pure spectral response curve of the semiconductor.
• Bandgap Estimation: Identification of the absorption edge from the spectral response curve, leading to an experimental approximation of the $\mathrm{CdS}$ bandgap energy ($E_g \approx 2.1 \pm 0.3$ $\mathrm{eV}$) at room temperature. The report discusses the distinct response regions resulting from surface recombination and bulk absorption effects.

Note: The detailed laboratory report is written in Greek, though the embedded mathematics, data tables, and plots follow universal scientific notation.

• Photoconductivity of CdS (PDF)