rus
Issue #6/2023
M.R.Sultanova, I.A.Remizov, A.A.Levchenko
INTERACTION OF INJECTED CHARGES WITH QUANTUM VORTICES IN SUPERFLUID HELIUM NEAR THE SURFACE
INTERACTION OF INJECTED CHARGES WITH QUANTUM VORTICES IN SUPERFLUID HELIUM NEAR THE SURFACE
DOI: https://doi.org/10.22184/1993-8578.2023.16.6.378.383
The motion of injected negative charges under free liquid surface, as well as in superfluid He-II volume at temperatures T ≈ 1.5 K in static electric fields of different configuration has been experimentally investigated. It is found, that in case of electric field configuration, which presses the charges to the He-II free surface there is a noticeable deviation of current density distribution from given by electric field, and in case of configuration when the charges move in the He-II volume, current density coincides with the electric field force lines.
The motion of injected negative charges under free liquid surface, as well as in superfluid He-II volume at temperatures T ≈ 1.5 K in static electric fields of different configuration has been experimentally investigated. It is found, that in case of electric field configuration, which presses the charges to the He-II free surface there is a noticeable deviation of current density distribution from given by electric field, and in case of configuration when the charges move in the He-II volume, current density coincides with the electric field force lines.
Теги: charged liquid surface quantum vortices subsurface charges superfluid helium заряды под поверхностью заряженная поверхность жидкости квантовые вихри сверхтекучий гелий
Original paper
INTERACTION OF INJECTED CHARGES WITH QUANTUM VORTICES IN SUPERFLUID HELIUM NEAR THE SURFACE
M.R.Sultanova1, Post-graduate / mabinkaiftt@issp.ac.ru
I.A.Remizov1, Researcher
A.A.Levchenko1, Director
Abstract. The motion of injected negative charges under free liquid surface, as well as in superfluid He-II volume at temperatures T ≈ 1.5 K in static electric fields of different configuration has been experimentally investigated. It is found, that in case of electric field configuration, which presses the charges to the He-II free surface there is a noticeable deviation of current density distribution from given by electric field, and in case of configuration when the charges move in the He-II volume, current density coincides with the electric field force lines.
Keywords: superfluid helium, subsurface charges, charged liquid surface, quantum vortices
For citation: M.R. Sultanova, I.A. Remizov, A.A. Levchenko. Interaction of injected charges with quantum vortices in superfluid helium near the surface. NANOINDUSTRY. 2023. V. 16, no. 6. PP. 378–383. https://doi.org/
10.22184/1993-8578.2023.16.6.378.383.
INTRODUCTION
Various ionic complexes can be formed in the liquid helium volume, the most common of which are positive and negative ions, as well as charged vortex rings [1]. Positive ions (cations) in liquid helium represent a helium atom without one electron surrounded by a layer of solidified helium due to polarization effects. The radius R+ of the cation is about 6 Å, and the effective mass of M+ is composed from the helium atom mass, solid helium sphere, and attached mass. Thus, the M+ mass of the positive ion is about 60–80 mHe4. A different structure has negative ions (anions), which are formed when an electron is introduced into liquid helium, creating a bubble, localizing inside a spherical cavity. Formation of electron bubbles is due to a number of reasons. Firstly, a helium atom is a stable quantum system that cannot attach an extra electron to itself, so a free electron is forced to move into the interatomic space near the individual atoms that repel it, having a large energy of zero vibrations [1]. Secondly, helium is characterized by a small value of surface tension at the liquid-vapor boundary. Thus, it is advantageous for the electron to form a bubble and thereby reduce its energy. Theoretical calculations show that the radius of the electron bubble R- is about 17 Å, and the effective mass of the anion almost coincides with its attached mass and is about 243 mHe4.
The drift velocity VD of positive and negative ions in a leading electric field of intensity E is described by the following dependence:
VD = μ · E, (1)
where μ is ion mobility in liquid helium, which depends on temperature [2]. The mechanism of the temperature dependence of ion mobility in liquid helium, as well as its dependence on the ion type, is described in detail in [1]. It is worth noting that when the charge moves in the liquid helium volume under the action of a leading electric field, and direction of the ion velocity at a point coincides with the vector of electric field strength, i.e., the ion mobility μ is a scalar. Thus, there is a local interaction of the ion with the pulling electric field.
It is known [3], that a force F of polarization origin (image force) acts on ions in liquid helium near the surface from the side of the liquid phase, which pushes ions from the surface boundary into the volume. When the electric field E⊥ pressing the ions to the surface is superimposed, a potential pit appears due to competition with the image force. Its minimum corresponds to the z0 coordinate:
. (2)
Therefore, ions introduced into helium localize on the surface z = z0, and turning the ion system into a two-dimensional one [3]. The charged surface can lead to essential dissipation of charges, which move near it.
In this work, the injected negative charges (electron bubbles) motion under free surface of the liquid and in the He-II superfluid volume at temperatures T≈1.5 K in static electric fields of different configurations is studied. It was found, that in the case of electric field configuration, which presses the charges to He-II free surface of there is a noticeable current density deviation from that given by the electric field, and in the configuration when the charges move in the He-II volume, and current density coincides with the electric field force lines.
RESEARCH METHODS
The experiments were carried out in a working cell, which was a rectangular parallelepiped with six electrically insulated faces with internal dimensions of 50 × 50 × 3 mm. The upper face of the cell was made of quartz glass, on the lower surface of which a semitransparent metallic film was sprayed. The distance "liquid surface – quartz glass" was 3 mm. A titanium-tritium radioactive charge source with a diameter of 3 mm was placed on one of the vertical faces of the cell (1 in Fig.1). A 5-segment collector was placed on the opposite side (3 in Fig.1). The segment width was 9 mm and the height was 30 mm. Each segment was connected to the independent current amplifier, and the output signals were digitized by an analog-to-digital converter (ADC) and recorded in computer memory. In the experiments, the time dependence of the collector current was measured when the plunger wave excitation was turned on and off. To estimate the constant component of the collector current Ii(t), and obtained experimental dependences were subjected to Fourier filtering at low frequencies.
A constant electric voltage was applied to the faces of the parallelepiped from independent sources relative to a common ground, so that the injected negative charges traveled from the charge source to the collector.
Wave excitation was performed using two flat plungers (2 in Fig.1) installed parallel to two adjacent faces of the cell at a distance of 3 mm. Each plunger was driven by a separate electromagnetic actuator, the alternating voltage to which was supplied from a two-channel functional generator. The plungers made progressive-return motion in the horizontal plane.
RESULTS
Fig.(2–4) shows the experimental time dependences of current on the segments of receiving collector Ii(t) before excitation of waves on the superfluid helium surface, during the operation of the plungers and after the pumping is switched off. The presented dependences were obtained at the following voltages on the cell faces: the voltage at the sources Usours1, 2 = –100 V, on the side face Uside1 = 0 V, voltage on the top face and bottom face varied during the experiment. In the presented experiments, harmonic pumping of waves on the liquid surface was carried out by two plungers at a frequency of 49.8 Hz. The phase difference of the electrical signals applied to the actuators was 90 °. The steepness of the waves generated on the surface was kH = 0.05.
Fig.2 shows the dependence obtained at the following voltages at the upper Uup = –50 V, and lower Udown = –100 V, faces of the cell. It can be seen that current is distributed among the first three segments –1, 0, 1 before the pump is turned on, and changes markedly with the pump turn-on. The current on segment –1 increases when the pump is turned on, while the current on segments 1, 0 decreases, and the total current increases noticeably.
Fig.3 shows the dependence obtained at the following voltages at the upper Uup = –100 V, and lower Udown = –50 V, faces of the cell. It can be seen that before pumping is turned on, the current mainly comes to the –1 segment of the receiver collector, and is approximately equal to the total current. With pumping turned on, the current distribution and total current do not change significantly. The current on the 0.1 segments remains approximately equal to zero during the entire measurement time.
Fig.4 shows the dependence obtained at the following voltages at the upper Uup= –50 V, and lower Udown = –100 V, faces of the cell, and at a completely filled cell without a free surface. In this case, the obtained dependences of the current on time look more noisy than in the previous cases, and when pumping is turned on, there is a burst of current on the -1 segment of the receiver collector and the total current. However, in general, the picture of current distribution looks similar to the one presented in Fig.3.
The dependences presented in Fig.2, 3 are obtained in experiments with different configuration of the electric field, so the charges moved at different distances from free surface, and in the experiments, the results of which are presented in Fig.4, there is no free surface.
Modeling of the electric field shows that at voltages on the upper Uup = –50 V, and lower Udown = –100 V, faces of the cell charges move near the two-dimensional charged surface, and at Uup = –100 V, Udown = –50 V their trajectories pass in the volume of liquid helium far from the surface.
It should be noted that when charges move away from the surface, or in a situation where the cell is completely filled with superfluid helium the current time dependences look the same, and the total current mainly comes to the -1 segment of the receiver collector. However, when the charges move near the surface, the current distribution before pumping is turned on is distributed as follows: –1 segment comes 33% to 0 segment 46%, and to 1 segment 21 %. Turning on the pumping leads to an increase in the total current of 35% and a significant change in its distribution to –1 segment comes 65% to 0 segment 22%, and to 1 segment 13% after turning off the pumping the distribution returns to the original one. Thus, presence of a free surface significantly affects the charge transport in superfluid helium, which can be attributed to charge dissipation on a charged two-dimensional liquid surface.
The dissipation of charges injected into liquid helium during wave excitation on the liquid helium surface was previously studied in our work [4]. According to [5], waves on the liquid surface lead to formation of Eulerian vorticity, and at high pumping amplitudes, individual vortices begin to overlap, forming vorticity shafts on which the injected charges are scattered.
CONCLUSIONS
Experimentally confirmed, that two-dimensionally charged surface of superfluid helium significantly influences onto the injected electrons transport.
ACKNOWLEDGMENTS
This work was supported by the grant of the Ministry of Science and Higher Education of the Russian Federation No. 075-15-2019-1893.
PEER REVIEW INFO
Editorial board thanks the anonymous reviewer(s) for their contribution to the peer review of this work. It is also grateful for their consent to publish papers on the journal’s website and SEL eLibrary eLIBRARY.RU.
Declaration of Competing Interest. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
INTERACTION OF INJECTED CHARGES WITH QUANTUM VORTICES IN SUPERFLUID HELIUM NEAR THE SURFACE
M.R.Sultanova1, Post-graduate / mabinkaiftt@issp.ac.ru
I.A.Remizov1, Researcher
A.A.Levchenko1, Director
Abstract. The motion of injected negative charges under free liquid surface, as well as in superfluid He-II volume at temperatures T ≈ 1.5 K in static electric fields of different configuration has been experimentally investigated. It is found, that in case of electric field configuration, which presses the charges to the He-II free surface there is a noticeable deviation of current density distribution from given by electric field, and in case of configuration when the charges move in the He-II volume, current density coincides with the electric field force lines.
Keywords: superfluid helium, subsurface charges, charged liquid surface, quantum vortices
For citation: M.R. Sultanova, I.A. Remizov, A.A. Levchenko. Interaction of injected charges with quantum vortices in superfluid helium near the surface. NANOINDUSTRY. 2023. V. 16, no. 6. PP. 378–383. https://doi.org/
10.22184/1993-8578.2023.16.6.378.383.
INTRODUCTION
Various ionic complexes can be formed in the liquid helium volume, the most common of which are positive and negative ions, as well as charged vortex rings [1]. Positive ions (cations) in liquid helium represent a helium atom without one electron surrounded by a layer of solidified helium due to polarization effects. The radius R+ of the cation is about 6 Å, and the effective mass of M+ is composed from the helium atom mass, solid helium sphere, and attached mass. Thus, the M+ mass of the positive ion is about 60–80 mHe4. A different structure has negative ions (anions), which are formed when an electron is introduced into liquid helium, creating a bubble, localizing inside a spherical cavity. Formation of electron bubbles is due to a number of reasons. Firstly, a helium atom is a stable quantum system that cannot attach an extra electron to itself, so a free electron is forced to move into the interatomic space near the individual atoms that repel it, having a large energy of zero vibrations [1]. Secondly, helium is characterized by a small value of surface tension at the liquid-vapor boundary. Thus, it is advantageous for the electron to form a bubble and thereby reduce its energy. Theoretical calculations show that the radius of the electron bubble R- is about 17 Å, and the effective mass of the anion almost coincides with its attached mass and is about 243 mHe4.
The drift velocity VD of positive and negative ions in a leading electric field of intensity E is described by the following dependence:
VD = μ · E, (1)
where μ is ion mobility in liquid helium, which depends on temperature [2]. The mechanism of the temperature dependence of ion mobility in liquid helium, as well as its dependence on the ion type, is described in detail in [1]. It is worth noting that when the charge moves in the liquid helium volume under the action of a leading electric field, and direction of the ion velocity at a point coincides with the vector of electric field strength, i.e., the ion mobility μ is a scalar. Thus, there is a local interaction of the ion with the pulling electric field.
It is known [3], that a force F of polarization origin (image force) acts on ions in liquid helium near the surface from the side of the liquid phase, which pushes ions from the surface boundary into the volume. When the electric field E⊥ pressing the ions to the surface is superimposed, a potential pit appears due to competition with the image force. Its minimum corresponds to the z0 coordinate:
. (2)
Therefore, ions introduced into helium localize on the surface z = z0, and turning the ion system into a two-dimensional one [3]. The charged surface can lead to essential dissipation of charges, which move near it.
In this work, the injected negative charges (electron bubbles) motion under free surface of the liquid and in the He-II superfluid volume at temperatures T≈1.5 K in static electric fields of different configurations is studied. It was found, that in the case of electric field configuration, which presses the charges to He-II free surface of there is a noticeable current density deviation from that given by the electric field, and in the configuration when the charges move in the He-II volume, and current density coincides with the electric field force lines.
RESEARCH METHODS
The experiments were carried out in a working cell, which was a rectangular parallelepiped with six electrically insulated faces with internal dimensions of 50 × 50 × 3 mm. The upper face of the cell was made of quartz glass, on the lower surface of which a semitransparent metallic film was sprayed. The distance "liquid surface – quartz glass" was 3 mm. A titanium-tritium radioactive charge source with a diameter of 3 mm was placed on one of the vertical faces of the cell (1 in Fig.1). A 5-segment collector was placed on the opposite side (3 in Fig.1). The segment width was 9 mm and the height was 30 mm. Each segment was connected to the independent current amplifier, and the output signals were digitized by an analog-to-digital converter (ADC) and recorded in computer memory. In the experiments, the time dependence of the collector current was measured when the plunger wave excitation was turned on and off. To estimate the constant component of the collector current Ii(t), and obtained experimental dependences were subjected to Fourier filtering at low frequencies.
A constant electric voltage was applied to the faces of the parallelepiped from independent sources relative to a common ground, so that the injected negative charges traveled from the charge source to the collector.
Wave excitation was performed using two flat plungers (2 in Fig.1) installed parallel to two adjacent faces of the cell at a distance of 3 mm. Each plunger was driven by a separate electromagnetic actuator, the alternating voltage to which was supplied from a two-channel functional generator. The plungers made progressive-return motion in the horizontal plane.
RESULTS
Fig.(2–4) shows the experimental time dependences of current on the segments of receiving collector Ii(t) before excitation of waves on the superfluid helium surface, during the operation of the plungers and after the pumping is switched off. The presented dependences were obtained at the following voltages on the cell faces: the voltage at the sources Usours1, 2 = –100 V, on the side face Uside1 = 0 V, voltage on the top face and bottom face varied during the experiment. In the presented experiments, harmonic pumping of waves on the liquid surface was carried out by two plungers at a frequency of 49.8 Hz. The phase difference of the electrical signals applied to the actuators was 90 °. The steepness of the waves generated on the surface was kH = 0.05.
Fig.2 shows the dependence obtained at the following voltages at the upper Uup = –50 V, and lower Udown = –100 V, faces of the cell. It can be seen that current is distributed among the first three segments –1, 0, 1 before the pump is turned on, and changes markedly with the pump turn-on. The current on segment –1 increases when the pump is turned on, while the current on segments 1, 0 decreases, and the total current increases noticeably.
Fig.3 shows the dependence obtained at the following voltages at the upper Uup = –100 V, and lower Udown = –50 V, faces of the cell. It can be seen that before pumping is turned on, the current mainly comes to the –1 segment of the receiver collector, and is approximately equal to the total current. With pumping turned on, the current distribution and total current do not change significantly. The current on the 0.1 segments remains approximately equal to zero during the entire measurement time.
Fig.4 shows the dependence obtained at the following voltages at the upper Uup= –50 V, and lower Udown = –100 V, faces of the cell, and at a completely filled cell without a free surface. In this case, the obtained dependences of the current on time look more noisy than in the previous cases, and when pumping is turned on, there is a burst of current on the -1 segment of the receiver collector and the total current. However, in general, the picture of current distribution looks similar to the one presented in Fig.3.
The dependences presented in Fig.2, 3 are obtained in experiments with different configuration of the electric field, so the charges moved at different distances from free surface, and in the experiments, the results of which are presented in Fig.4, there is no free surface.
Modeling of the electric field shows that at voltages on the upper Uup = –50 V, and lower Udown = –100 V, faces of the cell charges move near the two-dimensional charged surface, and at Uup = –100 V, Udown = –50 V their trajectories pass in the volume of liquid helium far from the surface.
It should be noted that when charges move away from the surface, or in a situation where the cell is completely filled with superfluid helium the current time dependences look the same, and the total current mainly comes to the -1 segment of the receiver collector. However, when the charges move near the surface, the current distribution before pumping is turned on is distributed as follows: –1 segment comes 33% to 0 segment 46%, and to 1 segment 21 %. Turning on the pumping leads to an increase in the total current of 35% and a significant change in its distribution to –1 segment comes 65% to 0 segment 22%, and to 1 segment 13% after turning off the pumping the distribution returns to the original one. Thus, presence of a free surface significantly affects the charge transport in superfluid helium, which can be attributed to charge dissipation on a charged two-dimensional liquid surface.
The dissipation of charges injected into liquid helium during wave excitation on the liquid helium surface was previously studied in our work [4]. According to [5], waves on the liquid surface lead to formation of Eulerian vorticity, and at high pumping amplitudes, individual vortices begin to overlap, forming vorticity shafts on which the injected charges are scattered.
CONCLUSIONS
Experimentally confirmed, that two-dimensionally charged surface of superfluid helium significantly influences onto the injected electrons transport.
ACKNOWLEDGMENTS
This work was supported by the grant of the Ministry of Science and Higher Education of the Russian Federation No. 075-15-2019-1893.
PEER REVIEW INFO
Editorial board thanks the anonymous reviewer(s) for their contribution to the peer review of this work. It is also grateful for their consent to publish papers on the journal’s website and SEL eLibrary eLIBRARY.RU.
Declaration of Competing Interest. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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