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DOE OSTI2026

Particle Acceleration and Pitch-angle Evolution in Relativistic Turbulence

Synchrotron radiation detected from relativistic astrophysical objects such as pulsar-wind nebulae and jets from active galactic nuclei depends on the magnetic fields and the distribution functions of energetic electrons in these systems. Relativistic magnetically dominated turbulence has been recognized as an efficient mechanism for structure formation and nonthermal particle acceleration in these environments. Recent numerical simulations of relativistic turbulence have provided insights into the energy distribution functions of accelerated electrons. Much less is currently understood about their pitch angle distributions, which are crucial for accurately interpreting the spectra of synchrotron radiation. We perform a detailed case study of the pitch angle distributions formed during the process of turbulent acceleration for B 0 /δB 0 = 10 and $\tilde{σ}$ 0 ~40, where B0 is the uniform component of the magnetic field, δB0 is the fluctuating component, and $\tilde{σ}$ 0 is the plasma magnetization based on the magnetic fluctuations. We find that even minimal numerical noise can cause substantial pitch angle scattering, but we demonstrate techniques for overcoming the numerical challenges associated with the evolution of very small pitch angles. Our numerical results are consistent with the phenomenological considerations found in C. Vega et al. (2024a, 2025).

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1959

Design Guide for Pitch-Up Evaluation and Investigation at High Subsonic Speeds of Possible Limitations Due to Wing-Aspect-Ratio Variations

A design guide is suggested as a basis for indicating combinations of airplane design variables for which the possibilities of pitch-up are minimized for tail-behind-wing and tailless airplane configurations. The guide specifies wing plan forms that would be expected to show increased tail-off stability with increasing lift and plan forms that show decreased tail-off stability with increasing lift. Boundaries indicating tail-behind-wing positions that should be considered along with given tail-off characteristics also are suggested. An investigation of one possible limitation of the guide with respect to the effects of wing-aspect-ratio variations on the contribution to stability of a high tail has been made in the Langley high-speed 7- by 10-foot tunnel through a Mach number range from 0.60 to 0.92. The measured pitching-moment characteristics were found to be consistent with those of the design guide through the lift range for aspect ratios from 3.0 to 2.0. However, a configuration with an aspect ratio of 1.55 failed t o provide the predicted pitch-up warning characterized by sharply increasing stability at the high lifts following the initial stall before pitching up. Thus, it appears that the design guide presented herein might not be applicable when the wing aspect ratios lower than about 2.0.

Spreemann, Kenneth P.↗

NASA NTRS1974

Mirroring within the Fokker-Planck formulation of cosmic ray pitch angle scattering in homogeneous magnetic turbulence

The Fokker-Planck coefficient for pitch angle scattering, appropriate for cosmic rays in homogeneous, stationary, magnetic turbulence, is computed from first principles. No assumptions are made concerning any special statistical symmetries the random field may have. This result can be used to compute the parallel diffusion coefficient for high energy cosmic rays moving in strong turbulence, or low energy cosmic rays moving in weak turbulence. Becuase of the generality of the magnetic turbulence which is allowed in this calculation, special interplanetary magnetic field features such as discontinuities, or particular wave modes, can be included rigorously. The reduction of this results to previously available expressions for the pitch angle scattering coefficient in random field models with special symmetries is discussed. The general existance of a Dirac delta function in the pitch angle scattering coefficient is demonstrated. It is proved that this delta function is the Fokker-Planck prediction for pitch angle scattering due to mirroring in the magnetic field.

Goldstein, M. L.↗

NASA NTRS1974

The Fokker-Planck coefficient for pitch-angle scattering of cosmic rays

For the case of homogeneous, isotropic magnetic field fluctuations, it is shown that most theories which are based on the quasi-linear and adiabatic approximations yield the same integral for the Fokker-Planck coefficient for the pitch-angle scattering of cosmic rays. For example, despite apparent differences, the theories due to Jokipii and to Klimas and Sandri yield the same integral. It is also shown, however, that this integral in most cases has been evaluated incorrectly in the past. For small pitch angles, the errors in previous evaluations are fortuitously of minor importance. For large pitch angles, however, these errors become more significant; and for pitch angles of 90 deg, the actual Fokker-Planck coefficient contains a delta function which has been overlooked in the past. The implications of these corrections on the possibility of relating cosmic-ray diffusion coefficients to observed properties of the interplanetary magnetic field are discussed.

Fisk, L. A.↗

NASA NTRS1973

Pitch paper pilot revisited

Two methods are described for predicting the handling qualities of an aircraft in pitch. Both methods are based on minimizing a pilot rating expression with respect to free pilot parameters. In one case the pilot rating expression was developed from a set of moving base simulation data. In the other case, the pilot rating expression was developed from a set of fixed base simulation data. In both cases pilot rating is primarily a function of pitch attitude and pitch rate; however, in the moving base case, the pilot rating is more sensitive to pitch rate than in the fixed base case. For each method, predicted pilot ratings and performance measures agree well with the measured data corresponding to that case. Both methods are used to predict pilot ratings for a set of flight test configurations and the results of the two methods agree to within one half a rating unit. The predicted ratings in both cases correlate well with the actual pilot ratings from the flight tests.

Arnold, J. D.↗

NASA NTRS1974

Human spatial orientation in the pitch dimension

Two experiments were conducted. In Experiment I, each of eight Ss attempted to place himself at 13 different goal orientations between prone and supine. Deviations of achieved body pitch angles from goal orientations were determined. In Experiment II, each of eight Ss attempted to align a visual target with his morphological horizon while he was placed at each of the 13 goal orientations. Changes in settings of the target were examined. Results indicate that Ss underestimate body pitch when they are tilted less than 60 deg backward or forward from the vertical, overestimate body pitch when they are nearly prone, and accurately estimate body pitch when they are nearly supine. In contrast, Ss set the visual target maximally above the morphological horizon when they are tilted 30 deg forward from the vertical. The findings are discussed in terms of common and different physiological mechanism that may underlie judgments of these types.

Cohen, M. M.↗

NASA NTRS1975

Additional experiments with a four-bladed cyclic pitch stirring model rotor, part 2 of second yearly report

The four bladed pitch stirring rotor model was used in a rotor dynamic wake survey at zero advance ratio, covering 2 deg, 5 deg and 8 deg collective pitch settings. Dynamic wake data were taken in planes .12 and .20 radii below the rotor disk and are to be compared with analytical wake data with parameters to be identified from pitch stirring transients. The model was modified to perform such transients. The instrumentation developed for this purpose is described together with the method of data acquisition and with the test procedures. The hardware and software for several data handling systems are discussed. These systems extract from pitch stirring transients the parameters of analytical dynamic rotor wake models.

Hohenemser, K. H.↗

NASA NTRS1977

Dynamics of high-bypass-engine thrust reversal using a variable-pitch fan

The test program demonstrated that successful and rapid forward-to reverse-thrust transients can be performed without any significant engine operational limitations for fan blade pitch changes through either feather pitch or flat pitch. For through-feather-pitch operation with a flight inlet, fan stall problems were encountered, and a fan blade overshoot technique was used to establish reverse thrust.

Schaefer, J. W.↗

NASA NTRS1976

Reverse-thrust technology for variable-pitch fan propulsion systems

Tests conducted to develop the technology necessary to meet the unique reverse-thrust performance requirements of a variable pitch fan propulsion system are discussed. The losses and distortion associated with the air entering the fan and core compressor from the rear of the engine, the direction of fan blade pitch rotation for best reverse-thrust aeroacoustic performance, and engine response and operating characteristics during forward- to reverse-thrust transients are among the factors studied. The test results of several scale fan models as well as a full-size variable pitch fan engine are summarized. Results show the following: a flared exhaust nozzle makes a good reverse-thrust inlet; acceptable core inlet duct recovery and distortion levels in reverse flow were demonstrated; adequate thrust levels were achieved; forward- to reverse-thrust response time achieved was better than the goal; thrust and noise levels strongly favor reverse through feather pitch; and finally, flight-type inlets make the establishment of reverse flow more difficult.

Sagerser, D. A.↗

NASA NTRS1985

Prediction of wing aeroelastic effects on aircraft lift and pitching moment characteristics

The distribution of flight loads on an aircraft structure determines the lift and pitching moment characteristics of the aircraft. When the load distribution changes due to the aeroelastic response of the structure, the lift and pitching moment characteristics also change. Some estimate of the effect of aeroelasticity on stability and control characteristics, particularly lift and pitching moment, is required for use in aircraft simulation models for evaluation of flight characteristics. This presentation outlines a procedure to incorporate aeroelastic effects into lift and pitching moment data from wind tunnel tests. Results are presented which were obtained from applying this procedure to an aircraft with a very flexible transport-type research wing. The procedure described is generally applicable to all types of aircraft.

Eckstrom, C. V.↗

NASA NTRS1986

Large-Scale Advanced Prop-Fan (LAP) pitch change actuator and control design report

In recent years, considerable attention has been directed toward improving aircraft fuel consumption. Studies have shown that the high inherent efficiency previously demonstrated by low speed turboprop propulsion systems may now be extended to today's higher speed aircraft if advanced high-speed propeller blades having thin airfoils and aerodynamic sweep are utilized. Hamilton Standard has designed a 9-foot diameter single-rotation Large-Scale Advanced Prop-Fan (LAP) which will be tested on a static test stand, in a high speed wind tunnel and on a research aircraft. The major objective of this testing is to establish the structural integrity of large-scale Prop-Fans of advanced construction in addition to the evaluation of aerodynamic performance and aeroacoustic design. This report describes the operation, design features and actual hardware of the (LAP) Prop-Fan pitch control system. The pitch control system which controls blade angle and propeller speed consists of two separate assemblies. The first is the control unit which provides the hydraulic supply, speed governing and feather function for the system. The second unit is the hydro-mechanical pitch change actuator which directly changes blade angle (pitch) as scheduled by the control.

Schwartz, R. A.↗

NASA NTRS1987

Analysis of a fixed-pitch X-wing rotor employing lower surface blowing

Lower surface blowing (LSB) is investigated as an alternative to the variable blade pitch requirement for the X-wing Circulation Control (CC) rotor concept. Addition trailing edge blowing slots on the lower surfaces of CC airfoils provide a bidirectional lift capability that effectively doubles the control range. The operational requirements of this rotor system are detailed and compared to the projected performance attributes of LSB airfoils. Analysis shows that, aerodynamically, LSB supplies a fixed pitch rotor system with the equivalent lift efficiency and rotor control of present CC rotor designs that employ variable blade pitch. Aerodynamic demands of bidirectional lift production are predicted to be within the capabilities of current CC airfoil design methodology. Emphasis in this analysis is given to the high speed rotary wing flight regime unique to stoppable rotor aircraft. The impact of a fixed pitch restriction in hover and low speed flight is briefly discussed.

Schwartz, Alan W.↗

NASA NTRS1989

Reduction of blade-vortex interaction noise using higher harmonic pitch control

An acoustics test using an aeroelastically scaled rotor was conducted to examine the effectiveness of higher harmonic blade pitch control for the reduction of impulsive blade-vortex interaction (BVI) noise. A four-bladed, 110 in. diameter, articulated rotor model was tested in a heavy gas (Freon-12) medium in Langley's Transonic Dynamics Tunnel. Noise and vibration measurements were made for a range of matched flight conditions, where prescribed (open-loop) higher harmonic pitch was superimposed on the normal (baseline) collective and cyclic trim pitch. For the inflow-microphone noise measurements, advantage was taken of the reverberance in the hard walled tunnel by using a sound power determination approach. Initial findings from on-line data processing for three of the test microphones are reported for a 4/rev (4P) collective pitch control for a range of input amplitudes and phases. By comparing these results to corresponding baseline (no control) conditions, significant noise reductions (4 to 5 dB) were found for low-speed descent conditions, where helicopter BVI noise is most intense. For other rotor flight conditions, the overall noise was found to increase. All cases show increased vibration levels.

Brooks, Thomas F.↗

NASA NTRS1989

The separated flow field on a slender wing undergoing transient pitching motions

The flow field surrounding a delta wing undergoing a transient pitching motion was studied experimentally. Of particular importance was the location of the leading edge vortices over the surface of the wing. The study was conducted on a 70-deg sweep flat-plate delta wing pitched about its one-half chord position. It is found that the maximum pitch rate is the key factor involved in the amount of lag experienced by the vortex breakdown during the transient pitching motion.

Thompson, S. A.↗

NASA NTRS1990

Reduction of blade-vortex interaction noise through higher harmonic pitch control

Brooks, Thomas F.↗

NASA NTRS1990

Development of pitch angle anisotropy and velocity diffusion of pickup ion shell distribution by solar wind turbulence

The evolution of pitch angle anisotropy in initially isotropic spherical shell distribution of pickup ions subjected to a continuous influence of weak or moderate intrinsic solar wind turbulence is investigated using a physical model which assumes that the wave of the solar wind turbulence is propagating mainly in the direction parallel to the ambient magnetic field. It is shown that, because of the pitch angle dependence of the velocity diffusion process, a significant pitch angle anisotropy of pickup ion shell distribution develops in the early stage of the diffusion process. Although it is smeared out later on, the result can be of significant importance, especially if the pickup ion density is large, because the pitch angle anisotropy can excite collective instabilities and increase the wave level, thus accelerating the diffusion process.

Yoon, Peter H.↗

NASA NTRS1991

Pitch angle scattering of cometary ions into monospherical and bispherical distributions

Low frequency magnetic fluctuations generated by solar wind/cometary ion distributions cause pitch-angle scattering of cometary ions. The nature of this pitch angle scattering is examined by means of one-dimensional hybrid simulations, in which newborn ions are created at a constant rate, and for various injection angles, alpha, relative to the magnetic field. Pitch angle scattering in the quasi-perpendicular regime (alpha above 60 deg) results in a bispherical velocity distribution while in the quasi-parallel regime (alpha between 0 and 60 deg), pitch angle scattering can result in either a monospherical or bispherical distribution, depending on the injection angle and initial beam velocity.

Miller, Ronald H.↗

NASA NTRS1991

Pitch-angle scattering of cometary ions - Computer simulations

The relationships between the rate of pitch-angle scattering induced by wave-particle interactions and two parameters, alpha, and the cometary ion interjection rate, Lambda-j, are studied with the aid of one-dimensional electromagnetic hybrid computer simulations of homogeneous plasmas. The simulations are done with relatively weak ion injection rates commensurate with those in the distant environment of the Comet Halley. In response to the linear temporal growth of the fluctuating magnetic field energy, the injected ions pitch-angle scatter toward isotropy in both the quasi-parallel and quasi-perpendicular regimes. For the injection of cometary oxygen ions, the simulations show pitch-angle scattering rates that increase as the square root of the injection rate. The oxygen ion pitch-angle scattering rates are roughly twice as large at perpendicular injection, again in qualitative agreement with observations.

Gary, S. P.↗