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Over the last few decades, different types of plasma waves (e.g., the ion acoustic waves (IAWs), electrostatic solitary waves, upper/lower hybrid waves, and Langmuir waves) have been observed in the upstream, downstream, and ramp regions of the collisionless interplanetary (IP) shocks. These waves may appear as short-duration (only a few milliseconds at 1 au) electric field signatures in the in-situ measurements, with typical frequencies of ∼1–10 kHz. A number of IAW features at the IP shocks seem to be unexplained by kinetic models and require a new modeling effort. Thus, this paper is dedicated to bridging this gap in understanding. In this paper, we model the linear IAWs inside the shock ramp by devising a novel linearization method for the two-fluid magnetohydrodynamic equations with spatially dependent shock parameters. It is found that, for parallel propagating waves, the linear dispersion relation leads to a finite growth rate, which is dependent on the shock density compression ratio, as Wind data suggest. Further analysis reveals that the wave frequency grows towards the downstream region within the shock ramp, and the wave growth rate is independent of the electron-to-ion temperature ratio, as Magnetospheric Multiscale (MMS) in-situ measurements suggest, and is uniform within the shock ramp. Thus, this study helps in understanding the characteristics of the IAWs at the collisionless IP shocks.

 

Abstract Recent micro-CT scans have demonstrated a much larger magnetic nanoparticle distribution volume in tumors after localized heating than those without heating, suggesting possible heating-induced nanoparticle migration. In this study, a theoretical simulation was performed on tumors injected with magnetic nanoparticles to evaluate the extent to which the nanoparticle redistribution affects the temperature elevation and thermal dosage required to cause permanent thermal damage to PC3 tumors. 0.1 cc of a commercially available ferrofluid containing magnetic nanoparticles was injected directly to the center of PC3 tumors. The control group consisted of four PC3 tumors resected after the intratumoral injection, while the experimental group consisted of another four PC3 tumors injected with ferrofluid and resected after 25 min of local heating. The micro-CT scan generated tumor model was attached to a mouse body model. The blood perfusion rates in the mouse body and PC3 tumor were first extracted based on the experimental data of average mouse surface temperatures using an infrared camera. A previously determined relationship between nanoparticle concentration and nanoparticle-induced volumetric heat generation rate was implemented into the theoretical simulation. Simulation results showed that the average steady-state temperature elevation in the tumors of the control group is higher than that in the experimental group where the nanoparticles are more spreading from the tumor center to the tumor periphery (control group: 70.6±4.7 °C versus experimental group: 69.2±2.6 °C). Further, we assessed heating time needed to cause permanent thermal damage to the entire tumor, based on the nanoparticle distribution in each tumor. The more spreading of nanoparticles to tumor periphery in the experimental group resulted in a much longer heating time than that in the control group. The modified thermal damage model by Dr. John Pearce led to almost the same temperature elevation distribution; however, the required heating time was at least 24% shorter than that using the traditional Arrhenius integral, despite the initial time delay. The results from this study suggest that in future simulation, the heating time needed when considering dynamic nanoparticle migration during heating is probably between 19 and 29 min based on the Pearce model. In conclusion, the study demonstrates the importance of including dynamic nanoparticle spreading during heating and accurate thermal damage model into theoretical simulation of temperature elevations in tumors to determine thermal dosage needed in magnetic nanoparticle hyperthermia design.