Often, the interpretation of experiments concerning the manipulation of the energy distribution of laser-accelerated ion bunches is complicated by the multitude of competing dynamic processes simultaneously contributing to recorded ion signals. Here we demonstrate experimentally the acceleration of a clean proton bunch. This was achieved with a microscopic and three-dimensionally confined near critical density plasma, which evolves from a 1 µm diameter plastic sphere, which is levitated and positioned with micrometer precision in the focus of a Petawatt laser pulse. The emitted proton bunch is reproducibly observed with central energies between 20 and 40 MeV and narrow energy spread (down to 25%) showing almost no low-energetic background. Together with three-dimensional particle-in-cell simulations we track the complete acceleration process, evidencing the transition from organized acceleration to Coulomb repulsion. This reveals limitations of current high power lasers and viable paths to optimize laser-driven ion sources. Monoenergetic proton beams can be useful in many applications but their generation from laser irradiation of targets is challenging. Here the authors demonstrate a laser-accelerated proton bunch with improved density and energy resolution by using a refined target. The acceleration field is mediated via relativistic electrons, which induce MV/µm electric fields that vary in time and space. The correspondingly broad ion energy distributions could be narrowed by limiting the spatial extent of the ion reservoir on the surface of irradiated opaque foils7 or by the use of droplets9. Reducing the foil thickness to the order of the laser skin depth also resulted in non-monotonic, peaked distributions with improved efficiency at higher ion energies11. Such radiation pressure or related volumetric acceleration mechanisms12 have in common that the majority of electrons in the central part of the focus are coherently pushed by the light forces and then drag ions along. The experimentally observed ion signal, however, is typically blurred by superimposed ions from regions outside of this central part of the laser focus. The volumetric interaction of electrons with the laser field requires plasma densities around the critical density nc. Plasma densities above nc are opaque for the laser light. For densities smaller than nc plasmas are transparent. By virtue of their 10 µm wavelength CO2 lasers enable to access such realms with readily available gas targets14. The low density does however limit the accelerated particle numbers severely. Spatially limited targets, so-called mass-limited targets, have attracted severe interest in theory15 and experiment17.Providing intense bursts of swift ions has gained particular interestIn this work, we exploit a so far inaccessible target parameter space by irradiating isolated, levitated plastic spheres of 1 µm diameter with a PW laser of 1.054 µm wavelength. In the rising edge of the laser pulse, the sphere expands to a few micrometer-sized plasma of approximately critical density for the near-infrared laser pulse. The single proton bunch generated in the interaction contains a large fraction of all target protons and are accelerated to narrow energy bands down to 5 MeV full-width at half-maximum (FWHM). Central energies for consecutive laser shots range from 20 to 40 MeV.20 W/cm2 (the peak intensity in best focus would have amounted to 2 × 1021 W/cm2).The laser pulses provided by the PHELIX PW laser at GSI (see Methods) contained 150 J energy with a pulse duration of 500 fs and were focused to a diameter of 3.7 ± 0.3 µm (FWHM of intensity). Plastic spheres of 1 µm diameter and hollow spheres with an outer diameter of 1 µm and 100 nm wall thickness served as targets. The microscopic target size inhibited any kind of mechanical support. Hence, we used a Paul trap to levitate and position the targets. A direct opto-electronic feedback allowed us to position the targets with an accuracy of around ±1 µm in all three dimensions (see Methods). The dominant source of fluctuation in laser target overlap due to pointing jitter of the laser was minimized by placing the target 1 to 1.5 Rayleigh lengths out of focus, where the on-target peak laser intensity amounted up to 7 × 1018. The measured autocorrelation trace in Fig. 19, where the laser amplitude and phase in the center are disturbed by the target plasma and the outer regions are, depending on the size of plasma and laser focus, less or even not at all affected. We modeled the resulting intensity distributions at the plane of observation for different plasma dimensions , allowing single-shot angular resolved energy measurements and thus the absolute determination of differential proton spectra. In all laser shots, we measured proton kinetic energy distributions with narrow energy spreads. We observed no notable variation across the accessible angular range of ±4°, which we analyzed for four angles Fig. . Integra21 to support our experimental results quantitatively and elucidate the underlying microscopic processes in more detail. It turned out that in the case of two-dimensional simulations we were not able to reproduce the experimental findings for a wide parameter range. Due to the high computational cost of three-dimensional simulations we were limited just to one single simulation. The initial conditions for plasma density and laser intensity distribution are chosen in such a way to closely resemble the experimental ones (see Methods). In analogy to the experiments, we extract absolute differential proton spectra in forward direction . It is interesting to note that the energy peak position of the detaching proton bunch closely follows the red line superimposed in Fig. t  = −260 fs. It represents the cumulatively time and spatially integrated laser intensity, i.e. the laser energy that has passed through the plasma up until the respective time. The proportionality factor between the accumulated energy and central bunch energy is estimated in this case to 2.4 MeV/J. At t = −260 fs the bunch energy no longer follows this favorable scaling, which would otherwise result in a proton bunch with 163 MeV energy. Over the time the electron population in the target gets more and more depleted. Hence, the acceleration due to the electron jet is replaced gradually by Coulomb repulsion forces. Extracting the three-dimensional ion density distributions at time t = −230 fs, the further evolution of the proton bunch can be well described by considering pure Coulomb repulsion (see Methods). The time evolution of the proton energy distribution resulting from this calculation is visualized by the blue line in Fig. Encouraged by the quantitative agreement of the differential spectrum in Fig. ity Fig. . As obse10 protons in the generated bunch, equal to 14% of the initial reservoir (micro-sphere target) content. The simulations further suggest that the longitudinal proton bunch length is only 4 µm  level below −4 mbar. Final stabilization of the target position was achieved by electro-optical damping under vacuum conditions smaller than 10−5 mbar. Hereby, the target was illuminated by a 50 mW laser with 660 nm wavelength. Stray light from the particle was imaged by an tele-centric lens system onto a position sensitive diode (PSD). With a beam splitter a small fraction of this stray light was imaged onto a CCD camera. The PSD signal was used to damp the particle by superimposing additional fields on the trap electrodes. Overlap of the damped particle with the laser focus was ensured by the laser focus diagnostic. By the CCD signal we ensured that the target remained quiet and at the right position prior to a full system shot. Fifty milliseconds before irradiation of the target with the PHELIX laser mechanical shutters protected illumination laser, CCD, and PSD.We employed a linear Paul trap for target positioning Fig. . Axial cThe PMMA hollow spheres were produced by covering polystyrene spheres Fig.  with a PM2 of 2.8. Twenty micrometer after the focus a spherically symmetric electron density distribution In the case of a sub-focus-sized mass-limited target, the laser is able to partially pass the target undisturbed. Regions containing plasma change phase and amplitude of the laser. We simulated diffraction patterns for various density distributions and compared it to experimentally recorded patterns. The laser was modeled by a Gaussian intensity distribution. To mimic divergence and focal spot size we used an We employed a slit spectrometer in our experiment. Herby a magnetic field disperses different particle momenta spatially. Different particle species can have the same momentum. To obtain proton spectra we used degraders to prevent the carbon ions to reach the spectrometer (protons have a higher penetration depth than carbon ions with the same momentum). Heavy ion spectra (in our case carbon and oxygen) are sacrificed for spatial information. The magnetic slit spectrometer Fig.  consistsThe evaluation routine for the proton spectra will be presented exemplarily on shoot #11. We used Bas-TR image plates (IP) as detectors covered in 100-µm-thick aluminum foil. Parts of the detector were additionally covered with 1-mm-thick CR39 nuclear track detectors wrapped in 15-µm-thick aluminum. Positions of CR39 are shown in Fig. Lineouts of the PSL signal are shown in Fig. x, y, z) with 3456 × 4624 × 3456 cells, resolving each λ = 1053 nm, linear polarization in x and propagation in y. Focusing the laser pulse on target, a normalized field strength Particle-in-cell simulations were performed using a 0.2.0 pre-release of PIConGPU. The simulated 3D domain spans 104 × 139 × 104 µm (nc and variations in density profiles. Due to the symmetry assumptions of 2D simulations (infinite cylinders in the third dimension), these simulations were not conclusive and made 3D3V simulations necessary.The overall simulation run on 8000 Nvidia K20x GPUs on Titan (ORNL) for 42,000 time steps within 11.5 h. During runtime, 1 PByte of raw output was generated which was aggregated with ADIOS and on-the-fly compressed with zlib. Parallel post-processing was performed on the Rhea cluster (ORNL), accessing the same file system. Extensive preparatory 2D3V simulations were executed on the cluster Hypnos (HZDR) with 8-16 Nvidia K80 GPUs, scanning the pre-expansion of the target from full density down to 0.016 t = −260 fs. The 3D maps were deduced from xy and yz density slices via interpolation. To account for neutralizing effects of bound electrons we reduced the carbon/oxygen charge density by the overlaying electron density. The so obtained 3D charge density distributions of carbons/oxygen and protons were used as input in a Coulomb repulsion code ). Starting velocities were assumed to be monoenergetic. We used mean kinetic energies extracted out of spectra from the simulation at t = −260 fs as starting parameters.We generated low resolution The data that support the plots within this article and other findings of this study are available from the corresponding authors on reasonable request. Additionally, 3D3V particle-in-cell simulation input parameters and data of Fig. Peer Review File


The aim of this experimental study was to evaluate which factors influence these CO2 indices in anesthetized spontaneously breathing horses. Six healthy adult horses were anesthetized in dorsal recumbency breathing spontaneously for 3 h. Data to calculate the CO2 indices (response variables) and dead space variables were measured every 30 min. Bohr’s physiological and alveolar dead space variables, cardiac output (CO), mean pulmonary pressure (MPP), venous admixture 2 indices before V/QEng and the explanatory variables with rho were reported. Multiple linear regression analysis was performed on P(a-ET)CO2 and VDalvfrac assessing which explanatory variables best explained the variance in each response. The simplest, best-fit model was selected based on the maximum adjusted R2 and smallest Mallow’s p (Cp). The R2 of the selected model, representing how much of the variance in the response could be explained by the selected variables, was reported. The highest correlation was found with the alveolar part of V/QEng to alveolar tidal volume ratio for both, P(a-ET)CO2 (r = 0.899) and VDalvfrac (r = 0.938). Venous admixture and CO best explained P(a-ET)CO2  and VDalvfrac . Adding MPP (P(a-ET)CO2) and airway dead space  to the models improved them only marginally. No “real” dead space variables from Bohr’s equation contributed to the explanation of the variance of the two CO2 indices. P(a-ET)CO2 and VDalvfrac were closely associated with the alveolar part of V/QEng and as such, were also influenced by variables representing a dysfunctional pulmonary perfusion. Neither P(a-ET)CO2 nor VDalvfrac should be considered pulmonary dead space, but used as global indices of V/Q mismatching under the described conditions.The arterial to end-tidal CO Ventilation/perfusion (V/Q) mismatch develops rapidly in anesthetized horses . Venous 2) difference and PaO2/inspiratory fraction of oxygen (FiO2) ratio or f-shunt have been tested to estimate venous admixture in people and horses (2 [P(a-ET)CO2], which was evaluated in spontaneously breathing and ventilated people several decades ago ((a-ET)CO2 was divided by PaCO2 and denoted as an estimate of alveolar dead space, and called alveolar dead space fraction [VDalvfrac = P(a-ET)CO2/PaCO2]  and the mean alveolar CO2 (PACO2) /PACO2]. As PACO2 was difficult to obtain, Enghoff suggested more than 50 years later that the partial pressure of CO2 in the arterial blood would be representative of the PACO2. Therefore, he modified Bohr’s formula substituting PACO2 by PaCO2 to derive the following formula: VDEng = (PaCO2 − PĒCO2)/PaCO2 CO2 and VDalvfrac is valid representative of pulmonary dead space used VDEng as their reference values for dead space CO2 and VDalvfrac to predict dead space or changes thereof ((a-ET)CO2 and VDalvfrac are venous admixture and atelectasis formation  in this manuscript.“True” dead space measurements, however, include the measurement of mixed-expired partial pressure of CO (PACO2) . Bohr us2)/PaCO2 . What Enial side . This faad space –13. On are alike , 12. It  thereof –16. Follormation , 18. Fur2 values , 15, 19.2 variables needed for Bohr’s equation. Until two decades ago, mixed-expired CO2, which is employed in Bohr’s equation and Enghoff’s approach, could only be measured by using a mixing chamber or Douglas bag  divided by tidal volume  is the most commonly used set-up to measure VCap. The VCap monitors developed for humans cannot cope with the high inspiratory and expiratory flow rates in horses. In order to allow the use of these pneumotachographs during equine anesthesia a custom-made flow-partitioning device can be inserted between ETT and the Y-piece of the anesthetic breathing circle . Fo. Fo2 varg circle . This de(a-ET)CO2 and VDalvfrac in anesthetized spontaneously breathing horses in dorsal recumbency. We hypothesized that: (1) P(a-ET)CO2 and VDalvfrac is strongly associated with V/QEng and derived variables, but much less with “true” dead space variables derived from Bohr’s original formula, (2) P(a-ET)CO2 and VDalvfrac is highly influenced by venous admixture and other factors influencing lung perfusion.The aim of this study was to discern factors that best explain the variability in PThis experimental study had ethical approval by the local committee for animal experimentation of the Swiss government (TV-4985). It was part of an original study performed to evaluate the effects of CPAP in anesthetized horses . Only thSix horses were included in this experimental study out of the control group of a former study . Horses via the jugular vein in the pulmonary artery using pressure guidance to determine correct positioning.Before premedication, a 8F 110-cm angiography balloon catheter  was placed −1)  IV and phenylbutazone (4 mg kg−1) IV . Anesthesia was induced with diazepam (0.02 mg kg−1)  and ketamine (2 mg kg−1)  IV. After induction, a 26-mm internal diameter cuffed silicone ETT was inserted into the trachea and connected to a circle breathing system  after placing the horse on a mattress in dorsal recumbency. Anesthesia was maintained using isoflurane  in an oxygen/air mixture (inspiratory O2 fraction: FiO2 = 0.5). Medetomidine was infused as a continuous rate infusion (0.0035 mg kg−1 h−1). Ketamine (50–100 mg bolus) was administered IV in case of spontaneous movement.Premedication consisted of medetomidine  were used to measure standard cardiopulmonary parameters throughout anesthesia as well as mean pulmonary artery pressure. The pressure transducer was zeroed to atmospheric pressure and leveled at the height of the shoulder joint. New pressure transducers were used for each horse.−1 h−1 and hydroxyethyl starch  was started 2 h after induction (1 mL kg−1 h−1) to account for the expected fluid losses due to medetomidine. Dobutamine was infused intravenously to maintain mean arterial pressure between 75 and 85 mmHg.Ringer’s lactate  was infused at a rate of 10 mL kg2 (PaCO2) exceeded 100 mmHg (13.3 kPa) at any measurement point horses were excluded from further data acquisition and mechanical ventilation was started.If arterial PCOIn the original study all horses were anesthetized for 6 h but only data from the first 3 h were used in this study. At the end of the study period, horses were allowed to recover unassisted.All cardiovascular data including mean pulmonary pressure (MPP) were recorded every 30 min during the first 3 h of anesthesia . Cardiac output (CO) was measured in triplicate at T60, T120, and T180 using the lithium dilution technique  .A flow-partitioning device was placed between the ETT and the Y-piece of the circle system dividing the total flow into four parts by two flow splitting adapters connected to each other by means of four silicon tubes equipped with four identical human adult NICO capnograph connectors  . These c2, carbon dioxide tension (PCO2) and arterial hemoglobin concentration ([Hb]) analyzed immediately .At time points of cardiovascular evaluation, VCap and spirometry data were recorded for 3 min using the dedicated software Datacoll . Furthermore, simultaneous arterial and mixed venous blood samples were taken under anaerobic conditions at each of these time points and POin vitro experiment published elsewhere  and the accuracy of the pneumotachograph was verified with a 100-mL calibration syringe before and after all measurements . The accuracy of the volume measurement of the flow-partioning device used in our set-up in connection with the NICO device was verified in an lsewhere . The dif2 values into an Excel spread sheet, P(a-ET)CO2 and VDalvfrac were calculated. VCap data were imported into a custom-made macro routine in Excel  and the recorded breaths analyzed. The mean value of all recorded breaths per time point and horse was used for statistical analysis. Bohr’s dead space ratio (VDBohr) and V/QEng were calculated following curve approximation by the solver function according to Tusman et al. (aw) to alveolar tidal volume was calculated based on Bohr’s  and Enghoff’s  respective equations. Airway dead space was defined as the volume at the inflection point of the VCap curve and was normalized by the tidal volume (VDaw/VT). The slope of phase III of the volumetric capnogram (SIII) was determined. Venous admixture 2) were calculated using standard equations CO2 and VDalvfrac, the explanatory variables were grouped according to what physiologic state they best represented; VDBohr, VDalvBohr/VTalv, and VDaw/VT were considered “true” dead space variables; CO and MPP were considered variables related to pulmonary blood flow; 2 admixture to the arterial side; SIII was treated as a factor characterizing homogenity of lung emptying; and VT and VO2 were considered possible explanatory variables based on evidence in the literature.For the purpose of explaining the variance of the responses PEng, V/QalvEng/VTalv) and P(a-ET)CO2 and VDalvfrac were performed using Pearson’s correlation with rho reported for each variable. All data points from each horse were used. Multiple linear regression analysis was then performed on P(a-ET)CO2 and VDalvfrac, assessing all combinations of explanatory variables to determine which explanatory variables best explained the variance of each response. The simplest, best-fit model was selected based on the maximum adjusted R2 and the smallest Mallow’s p (Cp). The R2 of the selected model, representing how much of the variance in the response could be explained by the variance of the selected variables, was reported. Enghoff’s approach and the associated variables (representing high and low V/Q ratios) were not included in the multi-variate analysis as the aim of this analysis was to show if the two indices represent V/Q = ∞ and areas of high V/Q ratio, or V/Q = 0 and areas of low V/Q ratio.Initial explorations of the association between Enghoff’s variables  age of 10 ± 6 years and body weight of 539 ± 35 kg  completed the 3 h study period and complete data sets of all horses could be analyzed.Respiratory variables, VCap, and specific cardiovascular data of all horses are given in Table (a-ET) CO2 ranged from −1 to 39 mmHg with the highest values at T120 (one horse), T150 (two horses), and T180 (three horses).The PalvEng/VTalv and a moderate correlation of V/QEng, (a-ET) CO2 CO2 was best explained by R2 = 0.7516). Adding MPP to the model improved the explanation by additional 2% (R2 = 0.7860) (Table The variance of P0) Table .frac ranged from −0.02 to 0.36 with the highest values observed at the same time points as the highest P(a-ET)CO2, except in one horse. This horse had the highest P(a-ET)CO2 earlier than the others showing consistently lower COs than all other horses during the entire study period.VDalvfrac with V/QalvEng/VTalv was high and moderate with V/QEng and Correlation of VDalvt Figure ; Table 2frac was best explained by R2 = 0.7115). Adding VDaw/VT to the model improved the explanation by another 3% (R2 = 0.7444) CO2 and VDalvfrac.Neither Bohr’s dead space variables, nor SIII, VT, or VO(a-ET)CO2 and VDalvfrac can be used to estimate Enghoff’s approach, but do not represent “true” dead spaces as derived from Bohr’s equation in spontaneously breathing horses. The results of this study also support the second hypothesis in that venous admixture and factors related to pulmonary perfusion, like CO and pulmonary pressure influence P(a-ET)CO2 and VDalvfrac. Therefore, P(a-ET)CO2 and VDalvfrac did not represent V/Q = ∞  in these spontaneously breathing horses in dorsal recumbency, but a global mismatch in the pulmonary ventilation/perfusion ratio, a finding supported by studies in other species.The results of this study support the first hypothesis in that both indices, P2 and ETCO2 from the theoretical side every increase of the difference can have two causes: (1) a decrease in ETCO2 relative to PaCO2 or (2) any increase in PaCO2 relative to ETCO2. In the following, we want to discuss the physiologic background for both causes related to the results found in this study.Looking at the difference between PaCO(1)2 in relation to PaCO2 is indicative of an increase in ventilation of non-perfused  or poorly perfused (areas of high V/Q ratio) alveoli, resulting in an increase in physiologic dead space. This fact directed Nunn and Hill  will increase CO2 and VDalvfrac will also increase. Future studies will need to verify this assumption.No drop in ETCOes Table . This inincrease , 27–29. frac in our study was airway dead space. This parameter, which neither influences Enghoff’s nor Bohr’s equation, is derived from the VCap curve using mathematical modeling of the expired CO2 over the measured volume ((a-ET)CO2 and VDalvfrac; in a model simulating human physiology airway dead space was detected as one of two main factors, the second one being venous admixture, causing inaccuracies in the calculation of alveolar dead space when using these CO2 indices 2 and ETCO2, namely an increase in PaCO2 in relation to ETCO2, occurs when CO2 cannot be eliminated from the blood into the alveoli. This is the case when the blood flows through atelectatic lung tissue or areas with low V/Q ratios. This fact makes P(a-ET)CO2 and VDalvfrac highly variable in situations of high venous admixture ((a-ET)CO2 and VDalvfrac in horses with a broad range of venous admixture volumes. As horses develop extensive venous admixture during anesthesia . This spectrum represents the expected amount of venous admixture in anesthetized horses in dorsal recumbency ((a-ET)CO2 and VDalvfrac values. Strang et al. suggested that P(a-ET)CO2 can be used as an index of oxygenation as it correlated well with the amount of atelectasis in pigs seen on computed tomography being even more predictive of the amount of atelectasis than the most accepted oxygen index PaO2/FiO2 ratio ((a-ET)CO2 and an impaired oxygenation has also been shown by means of pulse oximetry in human cardiac patients CO2 and VDalvfrac are influenced by parameters determining lung perfusion even further, we tested the influence of CO and pulmonary arterial pressure, where especially high CO values increased P(a-ET)CO2 and VDalvfrac. The influence of CO on the two CO2 indices was very likely due to its direct effect on venous admixture. It is known that increases in CO increase pulmonary pressure whereby pulmonary vessels perfusing collapsed lung areas are recruited. The blood flowing through these vessels increase venous admixture CO2 and VDalvfrac is not even well established in the human anesthesia literature (2 indices are still frequently used in equine anesthesia to estimate pulmonary dead space ((a-ET)CO2 and VDalvfrac in horses like duration of anesthesia, body weight, dorsal recumbency, and ventilation mode are known to influence venous admixture, CO, and/or pulmonary pressure. Our findings suggest that the idea of P(a-ET)CO2 or VDalvfrac being solely representative of dead space is erroneous or at least questionable in cases of high venous admixture typically observed in anesthetized horses.Our results also confirm earlier findings in humans that both COariables . The facariables , 31, 35.terature , 30, 31 ad space . There aad space , 37–39. 2 indices with V/QEng and V/QalvEng/VTalv suggests that P(a-ET)CO2 or/and VDalvfrac might be good estimates of global V/Q mismatching in horses. This assumption is based on the fact that variables based on Enghoff’s approach have been shown to represent the sum of dead space and venous admixture ((a-ET)CO2 or VDalvfrac with an adequate oxygenation (PaO2) might indicate a high physiological dead space, which points toward low CO and/or overdistension of lung tissue during controlled mechanical ventilation and recruitment maneuvers or even lung embolism CO2 or/and VDalvfrac might point toward high The high correlation found in this study between the two COdmixture , 16. Thiembolism , 40. On 2, and SIII on the two CO2 indices as they might have caused changes in the arterial and end-tidal CO2 difference CO2, or VDalvfrac represent global indices of the inefficiency of gas exchange and V/Q mismatching, and both are affected by venous admixture in healthy, anesthetised, spontaneously breathing horses. Under such conditions, the indices should not be used to estimate pulmonary dead space.Both COThis experimental study was carried out in accordance with the recommendations of the ARRIVE guidelines and had ethical approval by the local committee for animal experimentation of the Swiss government (TV-4985).All authors contributed to conception and design of research. MM, UA, and RB performed experiments. AR, SB, GH, GT, and JS analyzed data and did statistical analysis. All authors interpreted results. MM, SB, AR, GT, and JS drafted manuscript. All authors edited, revised, and approved final version of the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Here we utilize a non-Fourier approach to model buoyancy aiding or opposing flow of Maxwell fluid in the region of stagnation-point towards a vertical stretchable surface. Flow field is permeated by uniform transverse magnetic field. Two different heating processes namely (i) prescribed surface temperature (PST) and (ii) constant wall temperature (CWT) are analyzed. Through suitable transformations, the similarity equations are formed which are treated numerically for a broad range of magnetic interaction parameter. The obtained solutions are compared with available articles under limiting situations and such comparisons appear convincing. The structure of boundary layer depends on a parameter measuring the ratio of free stream velocity to the stretching sheet velocity. The momentum transport via stretching boundary is opposed by both fluid relaxation time and magnetic interaction parameter. Thermal boundary layer expands as the effects of transverse magnetic field and thermal relaxation time are amplified. A reduction in heat penetration depth is anticipated for increasing values of thermal relaxation time. The variation in wall slope of temperature with increasing thermal relaxation time appears similar at any assigned value of Prandtl number. A comparative study of aiding and opposition flow situations is presented and deliberated. Non-Newtonian fluids such as polymers, lubricants, granular materials, biological fluids etc. abound in daily life and in industrial processes, for example, in chemical, food processing and oil industries. The phenomenon and constitutive relations of such liquids are significantly varied and complex than the traditional viscous fluid dynamics. Viscoelastic materials display both viscous and elastic behaviors when subjected to the shearing force. The elastic effect arises due to existence of macromolecules such as polymer molecules which have a high relaxation time compared to characteristic time. Stress relaxation time is an important characteristic of these liquids which is the time required for the decay of elastic effects. Some common viscoelastic fluids are dough, yoghurt, cheese and gelled products. Viscoelastic fluid models of rate up involve one or more time derivatives and do not appear as explicit expression for stress tensor. In the past decade, Maxwell fluid model is frequently preferred by the researchers for the analysis of boundary layer problems. Maxwell fluid flow in the region of stagnation-point was analyzed by Sadeghy et al.  using spThe phenomenon of heat transfer has abundant applications in numerous practical fields such as cooling towers, food processing, dispersion of temperature/moisture across groove fields, cooling of small electrical components such as microchips in computer processors, nanofluid flows, solar water cooling, enhancing performance efficiency of diesel engine oil and various others. Heat conduction model developed by Fourier  is of imStagnation flows are particularly important in predicting drag coefficient near stagnation region of bodies in high speed flows. Fluid flow around a stagnation-point towards a stretchable sheet has been a compelling research topic because it is met in many metal working and polymer extrusion processes. The pioneering study of Heimenz  concerniInspired by the aforementioned studies, we intend to investigate the onset of mixed convection in Maxwell fluid flow due to heated or cooled vertical surface utilizing Cattaneo-Christov heat flux model. Flow field is influenced by vertical magnetic field of uniform strength. Studies presented through –47 demonu and v denoting velocity components along x− and y− directions in which the coordinate x extends along the sheet and y is normal to it. Let us assume that the surface stretches in x− direction with velocity uw(x) = ax and ue(x) = cx denotes the velocity of external flow where a and c are positive constants. The buoyancy force resulting due to density differences aids or opposes the external flow when it is directed towards or opposite to the external stream. The conducting Maxwell fluid is exposed to transverse magnetic field of strength B0 . The function Tw(x) = T∞ + bx prescribes the wall temperature in which b is a constant and T∞ represents the temperature of quiescent fluid. Utilizing the Oberback-Boussinesq approximation, equations representing Maxwell fluid motion with heat transfer are given below q)=−k∇T,in whichTy)=−∇⋅q,where λ1For detailed derivation of Eq , the reaConditions given in (6) indicates no-slip at the wall, condition (7) represent impermeability at the boundary, condition (8) indicates that viscous effects vanish at far distance from the surface and condition (9) signifies no temperature variation far from the boundary.ζ = y(a/ν)1/2, we seek the similarity solutions of (1), (2) and (5) of the following forms:Defining the non-dimensional horizontal distance Eq  is satisλ = Grx/Rex2 is the mixed convection parameter  in which Grx = gβT(Tw − T∞)x3/ν2 denotes the local Grashof number and Rex = uwx/ν is the local Reynolds number. For positive values of λ we have Tw > T∞ in the upper half (where x > 0) while Tw < T∞ in the lower half (where x < 0). In this situation, buoyancy force acts in the same direction as that of free stream velocity in both upper and lower halves, thereby assisting the fluid flow. For negative λ, buoyancy force is directed opposite to the external stream in both upper and lower halves. The other parameters appearing in (11) and (12)-(13) are given below:M denotes the magnetic interaction parameter, Pr denotes the Prandtl number, β stands for fluid relaxation time and γ for thermal relaxation time. A list of all symbols is shown in β = 0. Also, the analysis for usual Fourier law can be recovered by selecting γ = 0.In Eq , λ = Grxaring in  and 12)λ = Grx/Rand (12)- are givey1 = F,y2 = F′,y3 = F″,y4 = θ,y5 = θ′, an initial value problem consisting of five first order ordinary differential equations is obtained:Here we discuss the numerical treatment of governing Eqs.  and 12)12) usingζ∞, which is initially taken as low as 2 and then proceed with the numerical integration of system (16) by assigning suitable guesses for the missing slopes s1 = F″(0) and s2 = θ′(0). It means that a solution to the system (16) will depend on similarity variable ζ and the missing slopes s1 and s2. Here the mesh size h = 0.01 is considered in numerical integration. Thus conditions for F′ and θ at infinity can be expressed as y2 − (c/a) = 0 and y4 = 0 respectively. These algebraic equations are solved for s1 and s2 by Newton’s method. Solutions for s1 and s2 are employed in (16) and the system is integrated at a higher ζ∞, say ζ∞ = 4. We repeat this process for different ζ∞ until the solutions for s1 and s2 become independent of ζ∞. In Newton’s method, computer code is designed to perform maximum 30 iterations. Our computations have shown that such number of iterations is sufficient to fulfill the desired tolerance of 10−7 in all the considered cases.We replace infinity (∞) by a number, say F″(0) are compared with those of Mahapatra et al.  denotes the velocity vector, g =  is gravitational acceleration, J = σ(E + V × B) denotes the current density in which B =  is the applied magnetic field and E denotes the electric field intensity, d/dt ≡ ∂/∂t + (V ⋅ ∇)V is the material time derivative and S is the extra stress tensor which obeys the following relation:Relevant equation governing the two-dimensional flow of incompressible Maxwell fluid along a vertical surface with transverse magnetic field can be expressed as follows:λ1 is the fluid relaxation time, A1 = (∇V) + (∇V)t is the first Rivlin-Ericksen tensor and D/Dt the convected time derivative. For any vector A, we have:Here S, let us assign the operator In order to eliminate t) to Eq . We obtax−component of Eq (Making use of definition (19) and boundary layer approximations, nt of Eq  is obtai