Energy Loss Formula Research Articles

Target polarization effect on energy loss of O<sup>5+</sup> ions near Bohr velocity in low density hydrogen plasma

Energy loss of ions near the Bohr velocity in plasma is one of the important topics in intense heavy ion beam driven high energy density physics and inertial confinement fusion. Based on the ions-plasma interaction experimental platform at HIRFL, this work shows the new experimental energy loss results of 1.07 MeV (~66.9 keV/u) O<sup>5+</sup> ions penetrating through a low-density partially ionized hydrogen plasma target (radio frequency plasma). The decrease of energy loss with free electron density increasing is found, which is very different from our previous result. The new experimental results are discussed by considering the theoretical models which involves the charge screening of projectiles in the partially ionized plasma and the target polarization effect-Barkas correction term. For the charge screening , the comparison between the momentum transfer under the Coulomb potential and that under the Debye potential is given, but due to the low ionization degree, the plasma screening effect seems not to be the main reason for the decrease of energy loss. For the target polarization effect , in the Bohr velocity regime, the Barkas correction term can play a key role in the ion-atom collisions. Modeling the Barkas correction term based on the proposed classical energy loss formula, the experimental data of ions in the gas target can be well fitted by the calculated values. In the partially ionized plasma, the frequent thermal electron collisions can give rise to the atomic excitation of plasma target, correspondingly the Barkas correction term changes: it decreases with the fraction of excited atoms increasing. As a result, the energy loss decreases in our experiment. In the stopping of highly charged ions in a partially ionized low-density plasma, the collisions between ions and free electrons can produce an enhanced energy loss according to previous studies. However, the target polarization effect, especially the atomic excitations, can significantly reduce the energy loss, which is observed in our experiment. Therefore, the interaction between ions and partially ionized plasma should be further studied, and the Barkas correction can be a very important term.

Using the Optical Glauber Monte Carlo Model to Calculate R<sub> <i> AA</i> </sub> Related Results Produced by the ATLAS Collaboration

The energy loss during jet quenching due to the existence of Quark Gluon Plasma (QGP) is calculated by Optical Glaube Monte Carlo model with data collected by ATLAS Collaboration using the LHC detector. An energy loss formula for this situation was modeled and took the form . The nuclear modification factor, RAA, for jets in a 208Pb + 208Pb nucleus collision with rapidity interval of ∣у∣=2.8 and the initial transverse momentum of 50 GeV ≤ pT ≤ 1000 GeV, are compared with various data plots produced by ATLAS Collaboration. RAA results are plotted in different centrality bins, which are defined by the distribution of number of participating nucleons Npart. The RAA value was found to slowly increase at lower transverse momenta and flatten out at higher transverse momenta. The model’s theoretical calculation results turned out to be similar to the plots produced by the ATLAS Collaboration using data from the LHC with small differences for higher systematic uncertainty events.

Simulation of ATLAS Collaboration’s Measurement Results of Jet P<sub>T</sub> Correlations in Pb + Pb Collisions at √<span style="font: 13px Tahoma;margin-left:-2px;margin-right:2px;border-top:1px solid black"><span>S</span><sub>NN</sub></span>&#61 2.76 TeV

In this article, a model based on Glauber Monte Carlo is built to simulate the procedure of jet quenching in Quark-Gluon Plasma (QGP). In this model, energy loss of jets in QGP is parametrized by two quantities: path length of jets in QGP, L, and the initial transverse momentum of the jet PT. The path length of each branch of the jet are labeled L1 and L2. As input data, original jet energy data of p + p collisions were obtained from CMS measurement. After being processed by our model, simulated Pb + Pb jet energy data could be given and were compared to the data of ATLAS’s measurement in Ref. [1]. Distributions of (1/N)dN/dxJ where xJ=PT2/PT1, also noted as “frequency”, are presented as a function of PT1 and collision centrality. As the final result, two different forms of energy loss formula were found, both of which have good adaptation to certain centrality and PT ranges.

Calculation and Simulation of Temperature and Pressure Loss in a Pipe

In order to draw pipeline temperature and pressure loss and the temperature difference between the fluid and temperature, using the pipeline energy loss formula and heat transfer formula, deduces the relationship between the factors such as temperature and pressure loss, with the influence of temperature factor pressure loss of pipeline temperature simulation analysis on fluid simulation software Flowmaster, to find out the relationship between temperature and pressure loss and temperature and the fluid temperature. The results show that the temperature pressure loss is positively related to the temperature difference. When the temperature difference is fixed, the higher the temperature of the fluid, the smaller the pressure loss and the greater the temperature loss. The result of simulation can provide some reference for improving the efficiency of pipeline transportation.

On Molière and Fermi–Eyges scattering theories in hadrontherapy

We consider the evaluation of lateral spread distributions of charged particle beams at therapeutic energies, due to an absorber in the form of a homogeneous slab or of a stack. We show that the Molière theory has the same degree of flexibility as the Fermi–Eyges, but is much more accurate and does not present particular computing difficulties with the energy loss formula we have employed. It is also shown that the non-Gaussian shape of the projected one dimensional (1D) distributions is not a complication for passing from the projected to the spatial two-dimensional (2D) distribution, if one assumes circular symmetry. All the calculations are compared with the results of the FLUKA code. The nuclear interaction is not considered here, because it is outside of the scope of this work.

Short path length pQCD corrections to energy loss in the quark gluon plasma.

Recent surprising discoveries of collective behaviour of low-pT particles in pA collisions at LHC hint at the creation of a hot, fluid-like QGP medium. The seemingly conflicting measurements of non-zero particle correlations and RpA that appears to be consistent with unity demand a more careful analysis of the mechanisms at work in such ostensibly minuscule systems. We study the way in which energy is dissipated in the QGP created in pA collisions by calculating, in pQCD, the short separation distance corrections to the well-known DGLV energy loss formulae that have produced excellent predictions for AA collisions. We find that, shockingly, the large formation time (compared to the 1/μ Debye screening length) assumption that was used in the original DGLV calculation, results in a highly non-trivial cancellation of correction terms. We investigate the effect of relaxing the large formation time assumption in the final stages of the calculation and find that, not only is the effect of the small separation distance correction important even in large (~ 5 fm) systems, but also that the correction term dominates over the leading term at high energies.

Short path length pQCD corrections to energy loss in the quark gluon plasma

The twin identifications of high-pT enhancement and low-pT collective behaviour in the shockingly small systems of interacting particles created in pA collisions calls for a detailed theoretical energy loss analysis. We study the way in which energy is dissipated in the QGP created in pA collisions by calculating the short path length corrections to the DGLV energy loss formulae that have produced excellent predictions for AA collisions. We find that, shockingly, because of the large formation time assumption (used in the DGLV calculation), a highly non-trivial cancellation of correction terms results in a null short path length correction to the DGLV energy loss formula. We investigate the effect of relaxing the large formation time assumption in the final stages of the calculation and find, because of the separation distance between production and scattering centre is integrated over from 0 to ∞, ≳ 100% corrections, even in the large path length approximation employed by DGLV.

Short Path Length Energy Loss in the Quark-Gluon Plasma from pQCD

An outline for research to be done is given. In the heavy ion experiments at RHIC and the LHC, it is widely believed that a state of matter known as the quark-gluon plasma (QGP) has been produced. The so-called hard particles, or particles with very high momentum that are produced as a consequence of the asymptotic freedom of QCD, can be used as tomographic probes of the QGP. We will study the way in which energy is dissipated in this QGP by calculating, in pQCD, short path length corrections to the well-known energy loss formulae. This calculation is necessary to address the discovery at the LHC that shockingly small systems appear to exhibit collective behaviour.

SU-E-T-279: Dose Enhancement Effect Due to Cerium Oxide Nanoparticles Employed as Radiation Protectants

Purpose: The goal of radiotherapy is to maximize radiation dose to diseased cells while minimizing radiation damage to normal tissues. In order to minimize damage to normal tissues, cerium oxide nanoparticles (nanoceria) are currently considered as a radioprotectant. However, some studies have reported concerns that nanoceria can also lead to radiotherapy dose enhancement due to the high atomic number of cerium, especially when used in conjunction with kV energy and brachytherapy sources. In this study, this concern is investigated to determine if the concentrations of nanoceria employed in in-vivo studies to confer radioprotection can engender a significant dose enhancement. Methods: Radiation with energies ranging from 50kVp to 140kVp is investigated in this work along with brachytherapy sources Pd-103 and I-125. A previously established theoretical model is used to calculate the dose enhancement factor (DEF). In this model, each cell is assumed to be a voxel of size (10 µm, 10 µm, 10 µm) with nanoceria homogeneously distributed among them. Electron energy loss formula of Cole is used to calculate energy (and hence dose) deposited by photoelectrons and Auger electrons in each tissue voxel due to irradiation of nanoceria. The DEF is defined as the ratio of the dose with and without nanoparticles. Results: DEF calculation results are smaller than 1.02 with dosages of nanoceria smaller than 0.645 mg/g, which is shown to be sufficiently protective by some previous in-vitro and in-vivo experiments. The brachytherapy sources show higher DEF's than kVp radiations. DEF peaks are consistent with K shell and L shell energies of cerium, 40 keV and 6 keV, respectively. Conclusion: The results show that for sufficiently radioprotective concentrations of nanoceria, there will be minimal DEF when used in conjunction with clinically applicable kV energy radiotherapy sources or brachytherapy sources.

Shooting string holography of jet quenching at RHIC and LHC

We derive a new formula for jet energy loss using finite endpoint momentum shooting strings initial conditions in SYM plasmas to overcome the difficulties of previous falling string holographic scenarios. We apply the new formula to compute the nuclear modification factor RAA and the elliptic flow parameter v2 of light hadrons at RHIC and LHC. We show furthermore that Gauss–Bonnet quadratic curvature corrections to the AdS5 geometry improve the agreement with the recent data.

The mechanical energy equation for total flow in open channels

The mechanical energy equation is a fundamental equation of a 1-D mathematical model in Hydraulics and Engineering Fluid Mechanics. This equation for the total flow used to be deduced by extending the Bernoulli's equation for the ideal fluid in the streamline to a stream tube, and then revised by considering the viscous effect and integrated on the cross section. This derivation is not rigorous and the effect of turbulence is not considered. In this paper, the energy equation for the total flow is derived by using the Navier-Stokes equations in Fluid Mechanics, the results are as follows: (1) A new energy equation for steady channel flows of incompressible homogeneous liquid is obtained, which includes the variation of the turbulent kinetic energy along the channel, the formula for the mechanical energy loss of the total flow can be determined directly in the deduction process. (2) The theoretical solution of the velocity field for laminar flows in a rectangular open channel is obtained and the mechanical energy loss in the energy equation is calculated. The variations of the coefficient of the mechanical energy loss against the Reynolds number and the width-depth ratio are obtained. (3) The turbulent flow in a rectangular open channel is simulated using 3-D Reynolds averaged equations closed by the Reynolds stress model (RSM), and the variations of the coefficient of the mechanical energy loss against the Reynolds number and the width-depth ratio are discussed.

Use of energy loss mechanisms to constrain Lorentz invariance violations

In light of recent and probably upcoming observations of very high energy astroparticles, such as those reported by the IceCube collaboration, we readdress the energy loss mechanism by Lorentz violating particles. We analytically show that Cohen-Glashow's formula for energy loss is connected with a Poisson distribution for the number of decays, whose large fluctuations prevent placing bounds on Lorentz invariance violations. However, this model ignores the sharp change in the decay width after each process. We propose replacing Poisson statistics with a new distribution that takes this into account. We study the average final energy and its fluctuations according to the new statistics, contrasting it with Cohen-Glashow's result, and discussing the reliability of energy loss mechanisms to constrain violations of Lorentz invariance.

Energy Loss Analysis of Flared Cuff for Branched Endovascular Graft Application

Flared cuff for branched stent-graft application remains a longstanding challenge in endovascular graft exclusion. Introducing various kinds of function to describe the curved surface of flared cuff has shown significances. The method based on the energy loss formula of fluid mechanics is used to minimize energy dissipation of each model representing different functions. Among the five models that are created in experiment, the performance of arc model is relatively more excellent. The energy loss analysis has a certain guiding on morphology optimization of branched graft.

Magnetic fields of spherical compact stars in modified theories of gravity:f(R)type gravity and Hořava-Lifshitz gravity

The stellar magnetic field configuration and solutions of Maxwell equations in the external background spacetime of a magnetized spherical stars in the Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity and in modified $f(R)$ gravity are studied. The star is modeled as a sphere consisting of perfect highly magnetized fluid with infinite conductivity and frozen-in magnetic field. With respect to solutions for magnetic fields found in the Schwarzschild spacetime star in modified gravity theories, enhancing corrections are added to the exterior magnetic field. The energy losses through magnetodipolar radiation of the rotating magnetized compact star within alternative gravity theories is also considered. The question of whether these models can be considered as an alternative theory for general relativity is also discussed through astrophysical application of the obtained magnetodipolar energy loss formula. Finally we analyze the role of general relativistic effect on the decay of a neutron star's magnetic field in modified theories of gravity.

Evaluation of plastic materials for range shifting, range compensation, and solid‐phantom dosimetry in carbon‐ion radiotherapy

Beam range control is the essence of radiotherapy with heavy charged particles. In conventional broad-beam delivery, fine range adjustment is achieved by insertion of range shifting and compensating materials. In dosimetry, solid phantoms are often used for convenience. These materials should ideally be equivalent to water. In this study, the authors evaluated dosimetric water equivalence of four common plastics, high-density polyethylene (HDPE), polymethyl methacrylate (PMMA), polyethylene terephthalate (PET), and polyoxymethylene (POM). Using the Bethe formula for energy loss, the Gottschalk formula for multiple scattering, and the Sihver formula for nuclear interactions, the authors calculated the effective densities of the plastics for these interactions. The authors experimentally measured variation of the Bragg peak of carbon-ion beams by insertion of HDPE, PMMA, and POM, which were compared with analytical model calculations. The theoretical calculation resulted in slightly reduced multiple scattering and severely increased nuclear interactions for HDPE, compared to water and the other plastics. The increase in attenuation of carbon ions for 20-cm range shift was experimentally measured to be 8.9% for HDPE, 2.5% for PMMA, and 0.0% for POM while PET was theoretically estimated to be in between PMMA and POM. The agreement between the measurements and the calculations was about 1% or better. For carbon-ion beams, POM was dosimetrically indistinguishable from water and the best of the plastics examined in this study. The poorest was HDPE, which would reduce the Bragg peak by 0.45% per cm range shift, although with marginal superiority for reduced multiple scattering. Between the two clear plastics, PET would be superior to PMMA in dosimetric water equivalence.

Collisional energy loss of heavy quarks

We develop a transport approach for heavy quarks in a quark-gluon plasma, which is based on improved binary collision rates taking into account quantum statistics, the running of the QCD coupling and an effective screening mass adjusted to hard-thermal loop calculations. We quantify the effects of in-medium collisions by calculating the heavy flavor nuclear modification factor and the elliptic flow for RHIC energies, which are comparable to radiative effects. We also derive an analytic formula for the mean collisional energy loss of an energetic heavy quark in a streaming quark gluon plasma.

New peculiarities in angular distribution of Cherenkov radiation from relativistic heavy ions caused by their stopping in radiator: numerical and theoretical research

A new method and theoretical base for calculation of the Cherenkov Radiation (ChR) angular distribution from relativistic heavy ions (RHI) taking into account stopping in radiator is suggested. Our method is based on the thin radiator approximation and the Bethe-Bloch formula for ionization energy loss (stopping) and provides fast calculations without using any special software. The simple formula for estimation of the ChR angular distribution width in vicinity of the Cherenkov angle taking into account RHI stopping in radiator is obtained. New peculiarities of ChR - dependence on the RHI charge and mass (isotopic effect), emission wavelength (index of refraction) and radiator length - are studied. These new features of ChR from RHI allow for their possible applications to simultaneously reconstruction of both velocity and charge of RHI penetrating through radiator and even to measure the masses of isotopes or radiator stopping power.

Gold nanoparticle-aided brachytherapy with vascular dose painting: Estimation of dose enhancement to the tumor endothelial cell nucleus

Theoretical microdosimetry at the subcellular level is employed in this study to estimate the dose enhancement to tumor endothelial cell nuclei, caused by radiation-induced photo/Auger electrons originating from gold nanoparticles (AuNPs) targeting the tumor endothelium, during brachytherapy. A tumor vascular endothelial cell (EC) is modeled as a slab of 2 μm (thickness) × 10 μm (length) × 10 μm (width). The EC contains a nucleus of 5 μm diameter and thickness of 0.5-1 μm, corresponding to nucleus size 5%-10% of cellular volume, respectively. Analytic calculations based on the electron energy loss formula of Cole were carried out to estimate the dose enhancement to the nucleus caused by photo/Auger electrons from AuNPs attached to the exterior surface of the EC. The nucleus dose enhancement factor (nDEF), representing the ratio of the dose to the nucleus with and without the presence of gold nanoparticles was calculated for different AuNP local concentrations. The investigated concentration range considers the potential for significantly higher local concentration near the EC due to preferential accumulation of AuNP in the tumor vasculature. Four brachytherapy sources: I-125, Pd-103, Yb-169, and 50 kVp x-rays were investigated. For nucleus size of 10% of the cellular volume and AuNP concentrations ranging from 7 to 140 mg/g, brachytherapy sources Pd-103, I-125, 50 kVp, and Yb-169 yielded nDEF values of 5.6-73, 4.8-58.3, 4.7-56.6, and 3.2-25.8, respectively. Meanwhile, for nucleus size 5% of the cellular volume in the same concentration range, Pd-103, I-125, 50 kVp, and Yb-169 yielded nDEF values of 6.9-79.2, 5.1-63.2, 5.0-61.5, and 3.3-28.3, respectively. The results predict that a substantial dose boost to the nucleus of endothelial cells can be achieved by applying tumor vasculature-targeted AuNPs in combination with brachytherapy. Such vascular dose boosts could induce tumor vascular shutdown, prompting extensive tumor cell death.

On the detection of TeV γ-rays from GRB with km3 neutrino telescopes - I. Muon event rate from single GRBs

This is a preliminary study to examine the prospect of detecting TeV photons from $\gamma$-ray bursts (GRB) using km-size neutrino telescopes, specifically for the ANTARES neutrino telescope. Although optimized to detect upgoing neutrino-induced muons, neutrino telescopes nevertheless have a potential to detect high-energy photons by detecting downgoing muons from the electromagnetic cascade induced by the interaction of TeV photons with the Earth's atmosphere. The photon energy spectrum of a GRB is modeled by a simple power law and is normalized by simple energy considerations. Taking into account the absorption of TeV photons by cosmic infrared backgrounds, an optical depth table calculated from a model by \cite{fin10} is used and the arriving number of photons on top of the Earth atmosphere is determined. Muon production in the atmosphere is determined by considering two main channels of muon production: Pion photoproduction and direct muon pair production. The muon energy loss during their traverse from the surface to the bottom of the sea is determined using the standard muon energy loss formula. Assuming different detector sizes, the number of detectable muons from single GRB events located at different redshifts and zenith distances is determined. The background is calculated assuming it consists primarily of cosmic ray-induced downgoing muons. The detection significance is calculated and it can be concluded that to obtain at least $3\sigma$ detection significance, a typical GRB has to be located at redshift $z \lesssim 0.07$ if the detector's muon effective area is $A^{\mu}_{\rm eff} \sim 10^{-2}\;{\rm km}^{2}$, or redshift $z \lesssim 0.15$, if the muon effective area is $A^{\mu}_{\rm eff} \sim 1\;{\rm km}^{2}$.

Gravitational radiation in Hořava gravity

We study the radiation of gravitational waves by self-gravitating binary systems in the low-energy limit of Ho\ifmmode \check{r}\else \v{r}\fi{}ava gravity. We find that the predictions for the energy-loss formula of general relativity are modified already for Newtonian sources: the quadrupole contribution is altered, in part due to the different speed of propagation of the tensor modes; furthermore, there is a monopole contribution stemming from an extra scalar degree of freedom. A dipole contribution only appears at higher post-Newtonian order. We use these findings to constrain the low-energy action of Ho\ifmmode \check{r}\else \v{r}\fi{}ava gravity by comparing them with the radiation damping observed for binary pulsars. Even if this comparison is not completely appropriate---since compact objects cannot be described within the post-Newtonian approximation---it represents an order of magnitude estimate. In the limit where the post-Newtonian metric coincides with that of general relativity, our energy-loss formula provides the strongest constraints for Ho\ifmmode \check{r}\else \v{r}\fi{}ava gravity at low-energies.