# Direct Preference Optimization of Video Large Multimodal Models from
Language Model Reward

Ruohong Zhang∗♠ Liangke Gui ♠♢
Zhiqing Sun♠ , Yihao Feng∇ , Keyang Xu△ , Yuanhan Zhang♡ , Di Fu♢ ,
Chunyuan Li♢ , Alexander Hauptmann♠ , Yonatan Bisk♠ , Yiming Yang♠
♠CMU LTI, ♢Bytedance, ∇UT Austin, △Columbia University, ♡NTU
Project Page: https://github.com/RifleZhang/LLaVA-Hound-DPO Equal
contribution.

###### Abstract

Preference modeling techniques, such as direct preference optimization (DPO),
has shown effective in enhancing the generalization abilities of large
language model (LLM). However, in tasks involving video instruction-following,
providing informative feedback, especially for detecting hallucinations in
generated responses, remains a significant challenge. Previous studies have
explored using large large multimodal models (LMMs) as reward models to guide
preference modeling, but their ability to accurately assess the factuality of
generated responses compared to corresponding videos has not been conclusively
established. This paper introduces a novel framework that utilizes detailed
video captions as a proxy of video content, enabling language models to
incorporate this information as supporting evidence for scoring video Question
Answering (QA) predictions. Our approach demonstrates robust alignment with
OpenAI GPT-4V model’s reward mechanism, which directly takes video frames as
input. Furthermore, we show that applying this tailored reward through DPO
significantly improves the performance of video LMMs on video QA tasks.

##  1 Introduction

This paper addresses the challenge of aligning LMMs, particularly in tasks
that involve video instruction following. Despite recent advancements in
reinforcement learning (RL) (Ouyang et al., 2022; Bai et al., 2022; Lee et
al., 2023; Sun et al., 2023b) and DPO (Rafailov et al., 2024; Chen et al.,
2024b; Hosseini et al., 2024), which have been effective in guiding LLMs
towards generating more honest, helpful, and harmless content, their
effectiveness in multimodal contexts remains limited. The critical obstacle
lies in developing a robust reward system capable of distinguishing preferred
responses from less preferred ones, especially when such responses are
generated based on video inputs. The challenge is further complicated by the
presence of hallucinations in generated content, stemming from the scarcity of
alignment data across different modalities (Liu et al., 2023b; Sun et al.,
2023a).

While human preference data is valuable, it is challenging to scale due to its
cost and labor-intensive nature, as highlighted by the LLaVA-RLHF (Sun et al.,
2023a) paper, which collected 10k human-evaluated instances at a considerable
cost of $3000. Existing approaches for distlling preferences, such as those
for image data using GPT-4V (Li et al., 2023d), encounter scalability issues,
especially for video inputs that require analyzing multiple frames. While Ahn
et al. (2024) leverage a supervised finetuning (SFT) model for self-
evaluation, the efficacy of the SFT model remains uncertain, particularly in
accurately assessing the factuality of responses in relation to their
corresponding videos.

To tackle the aforementioned challenges, we introduce a cost-effective reward
mechanism aimed at reliably evaluating the quality of responses generated by
video (LLMs), serving as a basis for further preference optimization. We
propose the use of detailed video captions as a proxy for video content,
enabling a language model analyze video content and assess the accuracy of an
LMM’s response to a related question and determine the presence of
hallucinations. The language model provides natural language feedback as a
chain-of-thought step, and generates a numerical score for reward,
facilitating a cost-effective feedback system.

However, high-quality video captions are essential for this process. To
mitigate the shortage of high-quality video captions, we have developed a
comprehensive video caption dataset, ShareGPTVideo, using a novel prompting
technique with the GPT-4V model, comprising 900k captions that encompass a
wide range of video content, including temporal dynamics, world knowledge,
object attributes, and spatial relationships. With this video caption dataset
available, we verify that our reward mechanism, which utilizes video captions
as a proxy, is well-aligned with evaluations derived from the more powerful,
albeit costlier, GPT-4V model-generated rewards. Employing this reward
mechanism as the basis for DPO algorithm, we train LLaVA-Hound-DPO that
achieves an 8.1% accuracy improvement over the SFT counterpart. This marks a
significant advancement in video LMM alignment and represents the first
successful application of a DPO method in this domain.

Our contributions are outlined as follows:

  1. 1.

We develop a large-scale, detailed video caption dataset, covering a wide
array of content. This dataset serves as a foundational resource for LMM model
training and research, facilitating advancements in video understanding tasks.

  2. 2.

We introduce a cost-effective method for evaluating video instruction-
following tasks, serving as enhanced evaluation of model performance.

  3. 3.

We demonstrate the effective application of DPO to improve model performance
by leveraging the language model feedback as reward, which substantially
improves the alignment of video LMM, establishing a new benchmark for SOTA
performance in video QA tasks.

##  2 Related Work

###  2.1 Large Multi-Modal Models

LMMs (Liu et al., 2023b; a; Bai et al., 2023; Chen et al., 2023; Li et al.,
2023a) have enabled instruction following across modalities by utilizing LLM
as backbones. In the context of video understanding, LLMs have been adapted to
process video content (Lin et al., 2023a; Zhang et al., 2023a; Maaz et al.,
2023; Li et al., 2023b; Luo et al., 2023; Liu et al., 2023c; Jin et al., 2024;
Ahn et al., 2024). Our work adots Video-LLaVA backbone, focusing on model
enhancement through preference modeling with the DPO technique.

###  2.2 Video-text Datasets

Existing video-text datasets typically provide brief sentences or mere
keywords as captions, as indicated by Bain et al. (2021); Wang et al. (2023);
Yu et al. (2019); Jang et al. (2017); Xu et al. (2016). Shvetsova et al.
(2023) uses automatic speech recognition to extract textual content from
videos, but it encounters alignment issues when the audio does not match or is
absent from the visual content. Video-ChatGPT (Li et al., 2023b) employs human
effort to create high-quality video instructions, albeit limited to the
ActivityNet domain with only 100k instruction pairs. Our work leverages the
GPT-4V model with specifically crafted prompts to produce detailed video
captions as community resource for LMM training.

###  2.3 Preference Modeling for LMMs

Preference modeling techniques are employed to enhance the utility of LMMs
while mitigating the issue of hallucination. Sun et al. (2023a) leveraged
Reinforcement Learning with Human Feedback (RLHF) and incorporated caption
information into the reward model to improve the assessment of factuality.
More recently, Ahn et al. (2024) used RL on AI feedback to improve video LMM
performance. For the image understanding, Li et al. (2023d); Gunjal et al.
(2023) introduced the application of DPO on the distilled rewards from GPT-4V
on a group of model outputs, while Zhao et al. (2023) created preference data
using ChatGPT to generate positive and negative pairs informed by detailed
image descriptions. Our contribution extends DPO to the video LMM alignment,
with the use of detailed captions as factual evidence for reward modeling.

Figure 1: Workflow diagram showing: a) the use of GPT-4V for creating a
detailed caption dataset for videos; b) generating video instruction data for
SFT; c) integrating captions into a feedback loop for factually-enhanced DPO,
improving the model’s performance on video instruction-following tasks.

##  3 Method

As shown in fig. 1, our methodology enhances video LMM alignment through DPO
method using rewards from a language model. We elaborate on constructing a
video caption dataset in section 3.1. Subsequently, in section 3.2, we discuss
the generation of video instruction data and the fine-tuning process of our
model. Lastly, section 3.3 details the incorporation of generated captions as
a feedback mechanism for DPO method to refine our model’s factual alignment in
video instruction-following tasks.

###  3.1 Prompting GPT-4V Model for Detailed Video Caption Distillation

The selection of dataset includes videos from three sources: the WebVid and
VIDAL datasets, which are general domain videos sourced from YouTube with 400k
and 450k sampled videos respectively, and the ActivityNet dataset, which adds
50k videos focusing on human activities. The three datasets together result in
a comprehensive collection of 900k videos. To accommodate the requirement that
GPT-4V only takes images as input, we preprocess videos by uniformly
extracting ten frames per video content. These frames are then concatenated
into a sequence to serve as a proxy for the video. This sequence is the input
into GPT-4V to generate a coherent caption for the represented video based on
the frame sequence. The prompt adheres to guidelines covering temporal
dynamics, world knowledge, object attributes, spatial relationships, aesthetic
assessments, etc., with the goal of comprehensively understanding the video
contents.

###  3.2 SFT with Generated Video Instruction Data from Detailed Caption

To generate video instruction-following data for SFT, we adopt a similar
methodology outlined in Video-ChatGPT (Li et al., 2023b). Specifically, we
first randomly sample 20k, 30k, 30k captions in our dataset from ActivityNet,
WebVid and VIDAL respective and then employ ChatGPT to generate three
question-answer pairs given each detailed video caption, resulting in a total
of 240k instruction data for finetuning. This approach ensures that the
instructional data remains factually consistent with the content of the
detailed captions. The specific prompting strategy used for this instruction
generation process is detailed in fig. 13.

Figure 2: Detailed illustration of the proposed factually-enhanced DPO method.

###  3.3 DPO with Feedback from Language Model as Reward

Acquiring high-quality preference data is both costly and labor-intensive.
Although GPT-4V is an effective model for reward distillation, its high cost,
slow performance, and limited accessibility hinder scalability, especially for
video inputs with multiple frames. We propose a cost-efficient method to
generate reward data for DPO using detailed video captions as supporting
evidence, as shown in fig. 2.

Initially, we randomly select a subset of 20k instruction pairs from the
dataset described in section 3.2. The SFT model uses these sampled questions
and their corresponding videos to generate six responses per input pair at a
temperature of $1.0$. This procedure results in 120k question-answer pairs,
which will be evaluated. Subsequently, we employ ChatGPT to process inputs
including a question, the ground truth answer, the model’s prediction, and a
detailed description serving as supportive evidence, with the prompt in fig.
15. This generates an output that includes a natural language explanation as
chain-of-thought step, followed by a numerical reward score on a scale from
$1$ to $5$, indicating the level of factual alignment and overall quality.

For each video and question pair, we randomly select an answer with a score
$\geq$ 3 as positive example, and an answer with a score below $3$ as
negative. Cases where all responses are uniformly scored above or below $3$
are excluded from the dataset. After the selection process, approximately 17k
training instances are compiled for DPO training. Formally, the dataset is
denoted as $\mathcal{D}_{DPO}=\\{(\mathcal{V},x,y_{w},y_{l})\\}$, where
$\mathcal{V}$ is the video, $x$ is the question, $y_{w}$ and $y_{l}$ are the
positive and negative responses. The DPO objective is defined as below:

$\mathcal{L}_{\mathrm{DPO}}\left(\pi_{\theta};\pi_{\mathrm{ref}}\right)=-\mathbb{E}_{\left(\mathcal{V},x,y_{w},y_{l}\right)\sim\mathcal{D}_{DPO}}\left[\log\sigma\left(\beta\log\frac{\pi_{\theta}\left(y_{w}\mid
x,\mathcal{V}\right)}{\pi_{\text{ref }}\left(y_{w}\mid
x,\mathcal{V}\right)}-\beta\log\frac{\pi_{\theta}\left(y_{l}\mid
x,\mathcal{V}\right)}{\pi_{\text{ref }}\left(y_{l}\mid
x,\mathcal{V}\right)}\right)\right]\,,$

where $\pi_{\theta}$ is the policy model to be optimized and $\pi_{\text{ref
}}$ is the base reference model, both models are initialized with SFT weights.
$\sigma$ is the logistic function and $\beta$ is set to $0.1$.

Our approach to reward assignment leverages detailed captions as a proxy for
video frames, offering both cost-effectiveness and efficiency. This method
incurs costs of less than $20, under a pricing model of $1.5 per million
tokens. In comparison, previous methods of preference data collection, such as
in Sun et al. (2023a), required an expenditure of $3,000 to gather 10k human
preference data points. Additionally, the method proposed by Li et al.
(2023d), which employs GPT-4V for reward data labeling, incurs a significantly
higher cost—$30 per million tokens—and demonstrates considerably slower
inference speeds.

Figure 3: Assessing Evaluator Quality Using Captions in Place of Frames. The
left figure shows the distribution of evaluation score differences between
ChatGPT (with caption as proxy) and GPT-4V (directly on frames) evaluations.
The right figure shows the rate of preference agreement between ChatGPT and
GPT-4V as evaluators.

##  4 Assessment of Evaluator with GPT-4V Caption as Evidence

To assess the effectiveness of our proposed reward assignment method, which
utilizes detailed captions as a proxy of actual video frames, we conducted a
comparative analysis with the GPT-4V, used as a video QA evaluator. The latter
reward system employs GPT-4V evaluation directly taking in video frames, a
question, and the model prediction as inputs, with detailed prompt in fig. 16.
Both reward systems follow the same set of guidelines for scoring reward.

To compare the two methods, we sample $200$ videos from each of the WebVid,
VIDAL, and ActivityNet datasets, each associated with one question and two
model predictions from our SFT model, with one preferred and one dispreferred
by ChatGPT. This results in $1,200$ examples, for which we used GPT-4V (with
the ”gpt-4-vision-preview” version) version to assign scores. Filtering
through the Azure API backend resulted in $196$, $151$, and $143$ videos from
each dataset, respectively, having both answers evaluated. The average scores
of all examples from ChatGPT and GPT-4V evaluations were $2.9$ and $3.5$
respectively, indicating a tendency of GPT-4V to yield slightly positive
evaluations. The Pearson Correlation Coefficient (PCC) of $0.47$ ($p<0.01$)
suggests a moderate positive correlation. In fig. 3 (left), the distribution
of the difference between ChatGPT and GPT-4V scores reveals that majority
($>75\%$) of ChatGPT scores fall within one standard deviation ($\sigma=1.31$)
of GPT-4V scores. Additionally, in fig. 3 (right), the agreement on preference
between ChatGPT and GPT-4V, excluding ties, exceeded $70\%$. These findings
cautiously support our benchmark’s applicability in video QA evaluation.
Further refinements for better alignment—such as incorporating Likert scales
Zhou et al. (2023) or GPT-4 evaluation—are areas for future research.

|  | Existing Video QA Benchmark from Maaz et al. (2023)
---|---|---
Methods | LLM Size | MSVD-QA | MSRVTT-QA | TGIF-QA
Acc. | Score | Acc. | Score | Acc. | Score
FrozenBiLM (Yang et al., 2022)$*$ | 1B | 32.2 | - | 16.8 | - | 41.0 | -
VideoLLaMA (Zhang et al., 2023a)$*$ | 7B | 51.6 | 2.5 | 29.6 | 1.8 | - | -
LLaMA-Adapter (Zhang et al., 2023b)$*$ | 7B | 54.9 | 3.1 | 43.8 | 2.7 | - | -
VideoChat (Li et al., 2023b)$*$ | 7B | 56.3 | 2.8 | 45.0 | 2.5 | 34.4 | 2.3
BT-Adapter Liu et al. (2023c)$*$ | 7B | 67.5 | 3.7 | 57.0 | 3.2 | - | -
Video-ChatGPT (Maaz et al., 2023) | 7B | 68.6 | 3.8 | 58.9 | 3.4 | 47.8 | 3.2
Chat-UniVi (Jin et al., 2023) | 7B | 70.0 | 3.8 | 53.1 | 3.1 | 46.1 | 3.1
VideoChat2 Li et al. (2023c) | 7B | 70.0 | 3.9 | 54.1 | 3.3 | - | -
Video-LLaVA Lin et al. (2023b) | 7B | 71.8 | 3.9 | 59.0 | 3.4 | 48.4 | 3.2
LLaMA-VID (Li et al., 2023e) | 7B | 72.6 | 3.9 | 58.7 | 3.4 | 49.2 | 3.3
LLaMA-VID Li et al. (2023e) | 13B | 74.3 | 4.0 | 59.8 | 3.4 | 50.8 | 3.3
VLM-RLAIF (Ahn et al., 2024)$*$ | 7B | 76.4 | 4.0 | 63.0 | 3.4 | - | -
LLaVA-Hound-SFT | 7B | 75.7 | 3.9 | 58.7 | 3.3 | 53.5 | 3.3
LLaVA-Hound-DPO | 7B | 80.7 | 4.1 | 70.2 | 3.7 | 61.4 | 3.5

Table 1:  Evaluation of Model Performance on Zero-Shot Video Question
Answering Benchmarks Using gpt-3.5-turbo-0613. Models denoted with $*$ have
their results directly sourced from their original publications. Caution is
advised when interpreting these results; see Appendix A for an in-depth
analysis of evaluation challenges. All other baseline models were reproduced
by our team.

##  5 Experimental Results

###  5.1 Model Architecture, Image Data Mix-up and Training Pipelines

We adopt Video-LLaVA (Lin et al., 2023a) as the backbone of our video LMM, but
our dataset and method can be applied to any other architectures as well.
Specifically, Video-LLaVA employs LanguageBind (Zhu et al., 2023) encoder for
image and video frame inputs, a MLP projector with 2 fully connected layers to
map visual embeddings into text space, and Vicuna Chiang et al. (2023) as
large language model. During training, we first initialize the projection MLP
layer with the same Video-LLaVA MLP weight. Then we follow the training stages
below:

Caption Pre-training Stage (LLaVA-Hound-PT): At pretraining stage, we use
captioning data including 650k image caption data from ALLaVA (Chen et al.,
2024a) and our distilled 900k video caption. We freeze the LanguageBind visual
encoder and fine-tune the MLP projector and LLM, with learning rate 2e-5 and
batch size 128.

SFT Stage (LLaVA-Hound-SFT): We use instructional data from both image and
video domain to fine-tune the model for instruction-following ability. Our SFT
model use 600k image instruction data from ALLaVA and our generated 240k video
instruction data, with learning rate 5e-6 and batch size 128.

DPO training Stage (LLaVA-Hound-DPO): We use the 17k preference data
introduced in section 3.3 for DPO training. Following Ivison et al. (2023), we
train our policy model for $3$ epochs with learning rate 5e-7, and a batch
size of 128, resulting in roughly 420 training steps. All the experiments are
performed on 8 A100 gpus.

###  5.2 Existing Benchmark Evaluation

#### Dataset and Testing Environment

We evaluate model performance on three benchmark datasets: MSVD-QA Chen &
Dolan (2011), MSRVTT-QA Xu et al. (2016), and TGIF-QA Jang et al. (2017),
using ChatGPT with version gpt-3.5-turbo-0611 to assess model predictions. The
evaluation prompts follow Maaz et al. (2023). In our experiment, we found that
different ChatGPT versions have high impact on absolute score of metric, but
the overall ranking of models is relatively stable. We select
gpt-3.5-turbo-0613 due to its closeness to the reported score in Video-LLaVA
paper. Further details on the selection rationale and evaluation pitfalls are
discussed in Appendix A.

#### Baseline Selection

Our selection criteria include video LMM models that have demonstrated SOTA
performance, specifically including Video-LLaVA, which is also our choice of
architecture. We consider other contemporaneous SOTA models with similar
reported performance levels to Video-LLaVA, yet have not been directly
compared in prior studies. A key consideration in our selection is the
availability of models with accessible code and checkpoints, which is crucial
for ensuring reproducibility of our findings. To this end, we replicate models
including Video-ChatGPT (Maaz et al., 2023), LLaMA-VID (Li et al., 2023e) (7B
and 13B), Chat-UniVi (Jin et al., 2023), and Video-LLaVA Lin et al. (2023b).
We adopt the results from additional baselines including FrozenBiLM (Yang et
al., 2022), VideoChat (Li et al., 2023b) and VideoLLaMA (Zhang et al., 2023a),
sourced from their original publication.

Figure 4: Examples from MSRVTT-QA and MSVD-QA showcase that our LLaVA-Hound-
DPO generates better responses, and reveal key limitations of the existing
benchmark evaluation.

#### Results

In table 1, our analysis shows that within the SFT models, LLaMA-VID-7B and
Video-LLaVA exhibit comparable performance, with LLaMA-VID-13B performing the
best. Our LLaVA-Hound-SFT model achieves comparable performance to LLaMA-
VID-13B. Incorporating preference modeling, LLaVA-Hound-DPO achieves an
average accuracy of $70.75\%$, surpassing LLaVA-Hound-SFT, which has an
average accuracy of $62.65\%$, by $8.1\%$. Furthermore, LLaVA-Hound-DPO,
enhanced by DPO, exhibits superior accuracy compared to VLM-RLAIF’s
performance achieved through reinforcement learning.

#### Error Analysis

Figure 4 illustrates two examples. In the left example, LLaVA-Hound-SFT
provides an accurate description of the video’s first half but introduces a
hallucination with the phrase “I’m not scared of space,” absent in the video
content. LLaVA-Hound-DPO yields a more accurate inference. In the right
example, both LLaVA-Hound-SFT and Video-LLaVA models produce incorrect
inferences, whereas LLaVA-Hound-DPO successfully correctly identifies the
subject in the video. More critically, these examples unveil two significant
issues within the current benchmark: (1) the auto-generated questions from
existing benchmark may be grammatically incorrect or even nonsensical, and (2)
the answers are limited to a single word, which is insufficient for evaluating
LMMs with long-form text generation. Such constraints in the ground truth
answers hinder the evaluation of crucial aspects like helpfulness and
hallucination detection.

###  5.3 Proposed Benchmark Evaluation with GPT-4V Caption as Supporting
Evidence

As a solution to the above limitations in existing benchmark evaluation, we
propose a new set of test questions for same videos in the benchmark datasets
with generated QA from detailed captions, illustrated in appendix D. Applying
the our reward system in section 4, we report the score from ChatGPT, and a
score value $\geq 3$ will be considered correct for accuracy calculation. This
new long-form QA evaluation potentially support diverse aspects in responses
including relevance, accuracy, clarity and completeness in prompt 16.

|  | Proposed Video QA Benchmark (In-domain)
---|---|---
No. | Methods | ActivityNet-QA | VIDAL-QA | WebVid-QA
Acc. | Score | Acc. | Score | Acc. | Score
[1] | Video-ChatGPT (Maaz et al., 2023) | 34.17 | 2.19 | 29.35 | 2.10 | 38.88 | 2.27
[2] | LLaMA-VID-7B (Li et al., 2023e) | 36.54 | 2.27 | 30.58 | 2.15 | 36.99 | 2.24
[3] | LLaMA-VID-13B (Li et al., 2023e) | 37.33 | 2.29 | 32.50 | 2.18 | 39.73 | 2.30
[4] | Chat-UniVi (Jin et al., 2023) | 39.35 | 2.32 | 31.40 | 2.16 | 40.05 | 2.31
[5] | Video-LLaVA Lin et al. (2023b) | 41.35 | 2.38 | 34.30 | 2.24 | 42.47 | 2.39
[6] | LLaVA-Hound-SFT | 66.62 | 3.05 | 60.50 | 2.88 | 71.07 | 3.17
[7] | LLaVA-Hound-DPO | 76.62 | 3.18 | 70.06 | 3.04 | 79.82 | 3.29
[8] |  LLaVA-Hound-PT \+ Image Inst. | 69.31 | 3.09 | 60.57 | 2.85 | 68.03 | 3.02
[9] |  LLaVA-Hound-PT \+ VChat | 67.34 | 3.02 | 62.33 | 2.89 | 68.98 | 3.00
[10] |  LLaVA-Hound-DPO \+ training MLP | 71.89 | 3.10 | 65.57 | 2.95 | 75.37 | 3.21
[11] |  LLaVA-Hound-SFT \+ Self-play | 64.11 | 2.85 | 56.28 | 2.68 | 67.89 | 2.95
[12] |  LLaVA-Hound-DPO w/ lr3e-7 | 71.13 | 3.08 | 64.90 | 2.92 | 73.25 | 3.17

Table 2:  Our proposed video QA benchmark evaluation on in-domain dataset
using gpt-3.5-turbo-0301, with detailed captions as supporting evidence.

| Proposed Video QA Benchmark (Out-of-domain)
---|---
Methods | MSVD-QA | MSRVTT-QA | TGIF-QA | SSV2-QA
Acc. | Score | Acc. | Score | Acc. | Score | Acc. | Score
Video-ChatGPT (Maaz et al., 2023) | 34.06 | 2.20 | 25.65 | 1.98 | 31.35 | 2.09 | 19.36 | 1.75
LLaMA-VID-7B (Li et al., 2023e) | 34.14 | 2.21 | 25.02 | 1.99 | 27.18 | 2.00 | 22.16 | 1.84
LLaMA-VID-13B (Li et al., 2023e) | 35.81 | 2.25 | 26.34 | 2.02 | 27.58 | 2.01 | 21.98 | 1.83
Chat-UniVi (Jin et al., 2023) | 35.61 | 2.23 | 25.89 | 2.01 | 33.23 | 2.13 | 20.59 | 1.79
Video-LLaVA Lin et al. (2023b) | 39.46 | 2.37 | 30.78 | 2.15 | 32.95 | 2.18 | 24.31 | 1.90
LLaVA-Hound-SFT | 66.99 | 3.09 | 57.82 | 2.85 | 66.13 | 3.07 | 35.07 | 2.23
LLaVA-Hound-DPO | 73.64 | 3.12 | 68.29 | 2.98 | 74.00 | 3.12 | 48.89 | 2.53
LLaVA-Hound-PT \+ Image Inst. | 65.19 | 2.96 | 48.66 | 2.52 | 53.83 | 2.62 | 29.60 | 2.04

Table 3:  Our proposed video QA benchmark evaluation on out-of-domain dataset
using gpt-3.5-turbo-0301, with detailed captions as supporting evidence.

Table 2 and table 3 shows the in-domain and out-of-domain evaluation. We use
”gpt-3.5-turbo-0301” for evaluation as it is the same version for constructing
DPO dataset. The model performance is more distinguishable from our evaluation
with Video-LLaVA performing the best among the other baseline models.

Video LMM without Video Instruction: [8] in table 2 is baseline trained with
only image instruction fine-tuned on LLaVA-Hound-PT, which achieves an average
accuracy of $65.97\%$, comparable to the LLaVA-Hound-SFT model’s $66.06\%$ in
in-domain QA scenarios. However, its performance significantly drops in out-
of-domain QA contexts ($49.32\%$ vs. $56.50\%$), suggesting that Video QA
training could potentially enhance generalization capabilities.

Quality of Generated SFT: [9] substitutes our generated video QA with the
Video-ChatGPT dataset for Video-LLaVA fine-tuning. A comparison between the
findings of [9] and [6] reveals a marginal performance disparity of $0.2\%$ in
average accuracy, indicating that the quality of our generated QA closely
parallels that of the existing video QA datasets. Given the similar quality in
SFT data, the large gain of [6] over [5] can be reasonably concluded from
large-scale pre-training on video captions.

Unfreeze MLP: The comparison between [10] and [7] reveals a significant
decrease in performance when the MLP is unfrozen during DPO training. Despite
this drop, however, the performance remains superior to that of the SFT
baseline.

Smaller Learning Rate: The comparison between [12] and [7] reveals that using
a smaller learning rate of 3e-7 (vs. 5e-7) results in a decreasing of model
performance. This highlights the future improvements by finding better
hyperparameters.

Self-Play vs. DPO: Chen et al. (2024b) introduced a self-play methodology for
DPO training, which designates ground truth answers as preferred and model-
generated responses as dispreferred. When comparing the results of [11] with
those in [6], a notable decrease in accuracy by $3\%$ from the SFT model is
observed, suggesting that self-play may be less effective for video LMM
alignment, and introducing reward model is helpful.

Figure 5: The left figure shows the test set accuracy of the DPO model w.r.t
the number of training epochs. The right figure shows a comparison of DPO
model performance as generator vs. ranker.

DPO Accuracy vs. Training Epochs. The left of fig. 5 depicts the
generalization performance of the model on out-of-domain video QA tasks with
respect to the number of training epochs. We observe a consistent enhancement
in model performance among datasets during the initial 0 to 2 epochs, with
peak performance materializing at around 2.5 epochs, which corresponds to 350
training steps.

DPO as Ranker vs. Generator. Following Hosseini et al. (2024), we compare the
performance of employing the DPO model as a ranker for candidate answers
produced by the SFT model, operating at a temperature setting of 1.0. As
depicted on the right in fig. 5, we illustrate the test accuracy progression
through the selection of the best among $N$ candidates by the DPO ranker.
Initial observations indicate that the SFT model, when set to a temperature of
1.0, demonstrates a reduced accuracy (43.3%) compared to that achieved through
greedy decoding (57.8%). A steady enhancement in performance is noted as the
number of candidates increases, plateauing at an accuracy of approximately 62%
with 64 candidates. This performance, however, falls short when compared with
the direct application of the DPO model for answer generation, which yields an
accuracy of 68.29%. This difference suggests the stronger generalization of
DPO model in answer generation, despite it is trained on a reward
classification loss. The contradictory results to Hosseini et al. (2024) may
be due to the difference of tasks, i.e. Math vs. Video QA. Refer to appendix E
for more results.

###  5.4 Analysis on Video Captioning Ability from Pre-training

|
---|---
Figure 6: The video caption ability w.r.t number of training data evaluated on
both in-domain and out-of-domain test videos using GPT-4V.

In Figure 6, we present the video captioning ability of models across various
datasets, with a total of 900k distilled data instances. GPT-4V is employed
for self-evaluation (fig. 14), serving as the upper-bound performance, while
the Video-LLaVA serves for comparative analysis, establishing a baseline.
Notably, Video-LLaVA is trained on 54k video QA data instances. However, our
first checkpoint, utilizing only 10% of the data, is trained on 90k high-
quality caption data instances, likely accounting for the observed performance
disparity in the video captioning task. Our results demonstrate that
incorporating more distilled data contributes to improved model performance
across both in-domain and out-of-domain datasets. Despite these improvements,
a performance discrepancy with the GPT-4V model remains. Further, we evaluate
the generalization potential in specific data subsets, as shown in fig. 7 in
the Appendix. These subsets reveal varying degrees of generalization
challenges for different types of dataset. For example, the WebVid subset,
which concentrates on relatively static scenes, necessitates less data for
effective training compared to the VIDAL subset, which is marked by dynamic
scene transitions and a diversity of video themes.

##  6 Conclusion

In this study, we propose an cost-effective reward system that utilizes
detailed captions as proxies for video content. Our findings demonstrate that
the reward scores is well-aligned with the evaluation metrics of GPT-4V, and
the incorporation of this reward mechanism enhances DPO training, resulting in
SOTA performance on video QA tasks.

##  7 Reproducibility Statement

The ensure reproducibility of our work, we plan to release the following
items:

  1. 1.

Distilled video captions with corresponding frames.

  2. 2.

The model weights including the pre-trained, SFT, and DPO models.

  3. 3.

Code for training and testing using existing and our proposed benchmark.

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##  Appendix A Effect of ChatGPT Version on Official Benchmark Evaluation

Methods | LLM Size | MSVD-QA | MSRVTT-QA | TGIF-QA | Summary
---|---|---|---|---|---
Acc. | Score | Acc. | Score | Acc. | Score | Avg Acc. | Rank
|  | gpt-3.5-turbo-0301 evaluation |  |
Video-ChatGPT (Maaz et al., 2023) | 7B | 78.62 | 4.00 | 71.67 | 3.63 | 56.31 | 3.45 | 68.87 | 6
LLaMA-VID (Li et al., 2023e) | 7B | 82.57 | 4.12 | 71.94 | 3.65 | 59.00 | 3.63 | 71.17 | 4
LLaMA-VID (Li et al., 2023e) | 13B | 83.72 | 4.16 | 73.63 | 3.68 | 59.72 | 3.66 | 72.36 | 3
Chat-UniVi (Jin et al., 2023) | 7B | 80.52 | 4.02 | 66.92 | 3.41 | 57.73 | 3.49 | 68.39 | 7
Video-LLaVA (Lin et al., 2023b) | 7B | 81.44 | 4.08 | 73.29 | 3.65 | 58.34 | 3.61 | 71.02 | 5
LLaVA-Hound-SFT | 7B | 85.65 | 4.10 | 73.85 | 3.62 | 64.98 | 3.65 | 74.83 | 2
LLaVA-Hound-DPO | 7B | 88.50 | 4.20 | 82.10 | 3.84 | 75.48 | 3.81 | 82.03 | 1
|  | gpt-3.5-turbo-0613 evaluation |  |
Video-ChatGPT (Maaz et al., 2023) | 7B | 68.55 | 3.80 | 58.90 | 3.36 | 47.83 | 3.21 | 58.43 | 6
LLaMA-VID (Li et al., 2023e) | 7B | 72.62 | 3.92 | 58.73 | 3.38 | 49.21 | 3.28 | 60.19 | 4
LLaMA-VID Li et al. (2023e) | 13B | 74.29 | 3.96 | 59.82 | 3.41 | 50.83 | 3.33 | 61.65 | 3
Chat-UniVi (Jin et al., 2023) | 7B | 70.01 | 3.79 | 53.08 | 3.14 | 46.09 | 3.12 | 56.39 | 7
Video-LLaVA (Lin et al., 2023b) | 7B | 71.75 | 3.88 | 58.97 | 3.39 | 48.39 | 3.24 | 59.70 | 5
LLaVA-Hound-SFT | 7B | 75.70 | 3.86 | 58.73 | 3.31 | 53.51 | 3.30 | 62.65 | 2
LLaVA-Hound-DPO | 7B | 80.73 | 4.07 | 70.15 | 3.66 | 61.38 | 3.46 | 70.75 | 1
|  | gpt-3.5-turbo-1106 evaluation |  |
Video-ChatGPT (Maaz et al., 2023) | 7B | 73.02 | 4.01 | 62.09 | 3.61 | 47.76 | 3.36 | 60.96 | 6
LLaMA-VID (Li et al., 2023e) | 7B | 75.49 | 4.08 | 62.09 | 3.61 | 51.72 | 3.47 | 63.10 | 4
LLaMA-VID (Li et al., 2023e) | 13B | 76.97 | 4.10 | 63.16 | 3.61 | 52.53 | 3.50 | 64.22 | 3
Chat-UniVi (Jin et al., 2023) | 7B | 72.22 | 3.92 | 55.02 | 3.35 | 48.16 | 3.31 | 58.47 | 7
Video-LLaVA (Lin et al., 2023b) | 7B | 74.76 | 4.04 | 62.70 | 3.60 | 51.21 | 3.45 | 62.89 | 5
LLaVA-Hound-SFT | 7B | 81.09 | 4.08 | 64.13 | 3.57 | 58.05 | 3.53 | 67.76 | 2
LLaVA-Hound-DPO | 7B | 86.05 | 4.23 | 76.75 | 3.85 | 70.02 | 3.71 | 77.61 | 1

Table 4: Performance Evaluation Across ChatGPT Versions on Zero-Shot Video
Question Answering Benchmarks. This table compares the performance of state-
of-the-art video LMMs evaluated under different ChatGPT versions. The absolute
performance metrics scored by ChatGPT vary by versions. However, the
comparative ranking of models under the same ChatGPT version is relatively
stable.

In Table 4, we show impact of using different ChatGPT versions on metric
scores within zero-shot video question answering benchmarks. Our analysis
reveals significant variations in the absolute scores across ChatGPT versions,
but based on the average accuracy metric, the relative ranking of models under
the same ChatGPT version shows consistency.

This comparison underscores a critical issue: many prior studies neglect to
specify the ChatGPT version used, potentially leading to inaccurate
conclusions during evaluation. We advocate for the explicit designation of the
ChatGPT version in future evaluations. Analysis from Table 4 indicates that
the version gpt-3.5-turbo-0613 aligns most closely with the performance of the
Video-LLaVA (Lin et al., 2023a) model, serving as the benchmark for model
performance comparison in our study.

##  Appendix B Evaluation of Captioning Ability from pre-training

|
---|---
Figure 7: Training subsets exhibit varying levels of generalization
difficulty. The WebVid subset (left) requires less data compared to the VIDAL
subset (right)

##  Appendix C Distilled Caption Demonstration

Figure 8: Dataset examples annotated by GPT-4V

##  Appendix D Video QA Dataset Demonstration

Figure 9: Comparing testing QA in existing benchmark with that in our proposed
new benchmark. Figure 10: Comparing testing QA in existing benchmark with that
in our proposed new benchmark, example 2.

##  Appendix E Additional DPO Results

Figure 11: Test Set Accuracy of the DPO Model vs. Training Epochs. The figure
illustrates a consistent trend in both in-domain and out-of-domain video QA,
with peak performance occurring at approximately epoch 2.5, equivalent to 350
training steps.

Figure 12: Comparison of DPO Model Performance: Ranker vs. Generator. The DPO
model serves as a ranker, assigning reward scores to candidate answers
generated by the SFT model with a temperature setting of 1.0. Employing the
DPO model directly for answer generation results in superior performance
compared to its use as a ranker.

##  Appendix F Prompts for GPT-4V and ChatGPT Queries

⬇

Task Instructions:

\parGiven a caption that summarizes the content of a video, generate three
question-answer pairs that relate directly to the information and context
provided in the caption. The questions should be grounded to the understanding
of the video content.

\parGuidelines for QA Generation:

\par1. Helpfulness: Answers should provide sufficient detail and depth to
fully address the question. They should include relevant explanations, or
context where appropriate, to enhance understanding.

\par2. Faithfulness: The answers must accurately reflect the information
presented in the video caption. Avoid speculation or the inclusion of
information not contained or implied by the caption to maintain the integrity
of the content.

\par3. Diversity: Craft questions that cover different aspects of the video
caption to provide a comprehensive understanding of the content. This includes
factual inquiries, inferential questions, and those that may elicit
explanatory responses.

\parInput Video Caption:

{caption}

\parOutput format:

Q1: <question1>

A1: <answer1>

Q2: <question2>

A2: <answer2>

Q3: <question3>

A3: <answer3>

Figure 13: ChatGPT for instruction generation.

⬇

Your role is to serve as an impartial and objective evaluator of a video
caption provided by a Large Multimodal Model (LMM). Based on the input frames
of a video, assess primarily on two criteria: the coverage of video elements
in the caption and the absence of hallucinations in the response. In this
context, ’hallucination’ refers to the model generating content not present or
implied in the video, such as incorrect details about objects, actions,
counts, or other aspects not evidenced in the video frames.

\parTo evaluate the LMM’s response:

\parStart with a brief explanation of your evaluation process.

Then, assign a rating from the following scale:

\parRating 6: Very informative with good coverage, no hallucination

Rating 5: Very informative, no hallucination

Rating 4: Somewhat informative with some missing details, no hallucination

Rating 3: Not informative, no hallucination

Rating 2: Very informative, with hallucination

Rating 1: Somewhat informative, with hallucination

Rating 0: Not informative, with hallucination

\parLMM Response to Evaluate

{LLM_response}

\parOutput format:

Judgment: <your judgment>

Score: <integer value rating>

Figure 14: GPT-4V evaluation prompt for video captioning.

⬇

Given the following inputs:

\par1. **Ground Truth Video Caption**: {caption}

2. **Question Related to the Caption**: {question}

3. **Ground Truth Answer**: {answer}

4. **Model Predicted Answer**: {prediction}

\parYour task is to evaluate the model’s predicted answer against the ground
truth answer, based on the context provided by the video caption and the
question. Consider the following criteria for evaluation:

\par- **Relevance**: Does the predicted answer directly address the question
posed, considering the information provided in the video caption?

- **Accuracy**: Compare the predicted answer to the ground truth answer. Does the prediction accurately reflect the information given in the ground truth answer without introducing factual inaccuracies?

- **Clarity**: Assess the clarity of the predicted answer. Look for issues such as repetition, unclear descriptions, or any grammatical errors that could hinder understanding.

- **Completeness**: Determine if the predicted answer fully covers the scope of the ground truth answer. Does it leave out critical information or does it include all necessary details?

\par**Output Format**:

Explanation: <brief judgement of prediction>

Score: <a integer score of quality from 1-5>

Figure 15: ChatGPT-Evaluation Prompt for Video Question Answering. This prompt
takes in a detailed caption, question, ground truth answer, and model
prediction, subsequently generating an assessment of the prediction’s quality
alongside a corresponding score based on predefined criteria. A score value
$\geq 3$ will be considered correct for accuracy calculation.

⬇

Your task is to act as an impartial and objective assessor of answers
generated by a Large Multimodal Model (LMM) for video-based questions.
Utilizing video frames, a posed question, and the model’s provided answer,
your evaluation should focus on the following aspects:

\par- **Relevance**: Does the predicted answer directly address the question
posed, considering the information provided in the video caption?

- **Accuracy**: Compare the predicted answer to the ground truth answer. Does the prediction accurately reflect the information given in the ground truth answer without introducing factual inaccuracies?

- **Clarity**: Assess the clarity of the predicted answer. Look for issues such as repetition, unclear descriptions, or any grammatical errors that could hinder understanding.

- **Completeness**: Determine if the predicted answer fully covers the scope of the ground truth answer. Does it leave out critical information or does it include all necessary details?

\par**Input**:

Question: {question}

Model Predicted Answer: {prediction}

\par**Output Format**:

Explanation: <brief judgement of prediction>

Score: <an integer score of quality from 1-5>

Figure 16: GPT-4V Evaluation Prompt for Video Question Answering. Together
with video frames input in GPT-4V API, this prompt takes in a question, and
model prediction, subsequently generating an assessment of the prediction’s
quality alongside a corresponding score based on predefined criteria. A score
value $\geq 3$ will be considered correct for accuracy calculation. This is
used to assess the quality of ChatGPT evaluation in fig. 15.


# Effect of ionization waves on dust chain formation in a DC discharge

L. S. Matthews1<EMAIL_ADDRESS>K. Vermillion1  P. Hartmann1,2  M.
Rosenberg3  S. Rostami1  E. G. Kostadinova1,4  T. W. Hyde1  M. Y. Pustylnik5
A. M. Lipaev6,7  A. D. Usachev6  A. V. Zobnin6  M. H. Thoma8  O. Petrov1,6,7
H. M. Thomas5  O. V. Novitskii9  1CASPER, Baylor University, One Bear Place
97316, Waco, TX 76798-7316, USA 2Institute for Solid State Physics and Optics,
Wigner Research Centre for Physics, P.O.Box. 49, H-1525 Budapest, Hungary
3Department of Electrical and Computer Engineering, University of California
San Diego, La Jolla, California 92093, USA 4Physics Department, Auburn
University, Auburn, Alabama, 36849, USA 5Institut für Materialphysik im
Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), Münchener Straße
20, 82234 Weßling, Germany 6Institute for High Temperatures, Russian Academy
of Sciences, Izhorskaya 13/19, 125412 Moscow, Russia 7Moscow Institute of
Physics and Technology, Institutsky Lane 9, Dolgoprudny, Moscow Region, 141700
Russia 8 I. Physikalisches Institut, Justus-Liebig-Universität Gießen,
Heinrich-Buff-Ring 16, 35392 Gießen, Germany 9 Gagarin Research and Test
Cosmonaut Training Center, 141160 Star City, Moscow Region, Russia

###### Abstract

An interesting aspect of complex plasma is its ability to self-organize into a
variety of structural configurations and undergo transitions between these
states. A striking phenomenon is the isotropic-to-string transition observed
in electrorheological complex plasma under the influence of a symmetric ion
wakefield. Such transitions have been investigated using the Plasma Kristall-4
(PK-4) microgravity laboratory on the International Space Station (ISS).
Recent experiments and numerical simulations have shown that, under PK-4
relevant discharge conditions, the seemingly homogeneous DC discharge column
is highly inhomogeneous, with large axial electric field oscillations
associated with ionization waves occurring on microsecond time scales. A
multi-scale numerical model of the dust-plasma interactions is employed to
investigate the role of the electric field on the charge of individual dust
grains, the ion wakefield, and the order of string-like structures. Results
are compared to dust strings formed in similar conditions in the PK-4
experiment.

##  1 Introduction

The PK-4 system is the latest generation in the line of microgravity dusty
plasma experiments currently in operation on-board the International Space
Station (ISS). Since its installation in the Columbus module in 2014, the PK-4
experiment has produced remarkable experimental data related to dust particle
enhanced plasma emission (Usachev et al., 2016, 2018), transverse ionization
instability (Zobnin et al., 2016), transformations of dust structures
(Polyakov et al., 2017), electrorheological and demixing phenomena (Dietz et
al., 2017), particle kinetics (Liu et al., 2018), structural phase transitions
(Dietz et al., 2018), and dust density waves (Jaiswal et al., 2018). Detailed
reviews of past and recent microgravity dusty plasma activities can be found
in Dietz et al. (2018); Thomas et al. (2019).

Besides these fundamental physical investigations, analysis of the raw
experimental data has shown that under some circumstances the dust particles
show a tendency for chain formation where the particles align into lines
several tens of particles long parallel to the discharge tube axis, as
reported in Pustylnik et al. (2016); Schwabe et al. (2019) and shown in figure
1. This happens most often (but not exclusively) when the polarity switching
is applied, in which the positive and negative polarities of the DC electrodes
are alternated at a frequency of typically 100-500 Hz, with the aim of
stabilizing the dust cloud in the field of view of the observing cameras.

Several previous experiments have produced structures with aligned grains.
Dust lane formation has been reported, e.g., during phase separation in binary
complex plasmas under microgravity (Sütterlin et al., 2009; Du et al., 2012),
driven by the electrostatic interaction between the charged dust grains in
relative motion. Vertical dust particle chains can routinely be prepared in
the electrode sheath region of a radio frequency (RF) gas discharge (Kong et
al., 2011, 2014; Chen et al., 2016), where particle alignment is stabilized by
the enhanced horizontal confinement provided by an open glass box and the ion
wake field due to the fast (supersonic) streaming of ions around the particles
(Hutchinson, 2011, 2012; Kompaneets et al., 2016). The electrorheological
effect (or the homogeneous-to-string transition) can also favor dust chain
formation as demonstrated by Ivlev et al. (2008, 2011). In this case the dust
particles are surrounded by the quasi-neutral plasma bulk, but due to an
externally applied alternating electric field and consequently streaming
(subsonic) ions, the Debye screening sphere around the dust particles becomes
distorted leading to an anisotropic inter-particle repulsion. Note that this
is different than the electrorheological effect in granular suspensions, which
results from polarization of the grains themselves (Kwon et al., 2015).

Among these known chain-forming processes, the electrorheological effect is
the most probable one to be acting in the positive column region of the PK-4
discharge plasma. For a PK-4 neon discharge at $p=50$ Pa and $I=1$ mA, the
experimentally determined plasma parameters yield an axial electric field
$E_{z}\simeq 2.2\pm 0.2$ V/cm, with an electron density $n_{\rm
e}\simeq(2.2\pm 0.2)\times 10^{8}$ cm-3 and electron temperature $T_{\rm
e}\simeq 7\pm 0.5$ eV (Usachev et al., 2004; Khrapak et al., 2012). Assuming a
stable positive column and based on the well-studied equilibrium transport
behavior of Ne+ ions in neutral Ne gas (Skullerud & Larsen, 1990), one can
estimate the ion drift velocity to be $v_{\rm id}\simeq 190$ m/s resulting in
a thermal Mach-number $M_{\rm th}=v_{\rm id}/v_{\rm th}=0.54$. Here the ion
thermal velocity is defined as $v_{\rm th}=\sqrt{k_{\rm B}T_{\rm i}/m_{\rm
i}}$ assuming a temperature of $T_{\rm i}=300$ K for the neon ions. The
thermal Mach number is the key quantity for the estimation of the strength of
the electrorheological effect based on the formula derived in Ivlev et al.
(2008) for the pairwise interparticle interaction energy

$W(r,\theta)\simeq\frac{Q^{2}}{4\pi\varepsilon_{0}}\left[\frac{{\rm
e}^{-r/\lambda_{\rm D}}}{r}-0.43\frac{M_{\rm th}^{2}\lambda_{\rm
D}^{2}}{r^{3}}\left(3\cos^{2}\theta-1\right)\right],$ (1)

where $r$ is the distance between two dust grains of charge $Q$ aligned in the
direction of the ion flow, $\theta$ is the angle relative to the ion drift
direction and $\lambda_{\rm D}$ is the unperturbed Debye screening length. In
this description the isotropic Yukawa (screened Coulomb) interaction is
modified by a dipole-like term and higher order contributions are neglected.
It has been shown in Ivlev et al. (2008) that anisotropy in the particle
distribution gradually starts to develop above a critical value of the thermal
Mach-number $M_{\rm cr}\simeq 0.3$ depending on the plasma conditions and that
apparent ordered chains build up at $M_{\rm th}>1$ with increasing length and
stability as the ion drift speed is further increased. Based on these previous
findings and the assumption of a stable DC positive column, it could be
expected that given the typical PK-4 conditions discussed above, the estimated
thermal Mach number of 0.54 is insufficient to result in the formation of long
particle chains, in contrast with the observed particle behavior. However,
recent simulations and experiments have shown that the plasma column supports
fast-moving ionization waves, with associated ion flows speeds $M_{th}>1$.
Although these variations in the plasma occur on the micro-second timescale,
they appear to have an influence on the dynamics of the dust grains, which
typically occur on a millisecond timescale.

In this work, we examine conditions affecting dust chain structure formation
in the PK-4 experiment based on realistic gas discharge modeling, dust
particle charging simulations, and calculations of the dust-dust and dust-ion
interactions. Of particular interest is the strong electric field created by
ionization waves which travel through the discharge column with a period on a
microsecond timescale. A description of the PK-4 experiment and plasma
conditions determined by a numerical model of the gas discharge are given in
Section 2, with a description of the molecular dynamics (MD) model of the ion
and dust dynamics in Section 3. The dust charge and configuration resulting
from applying different time-averaged discharge conditions are given in
Section 4. These results are compared with observations from the PK-4
experiment in Section 5. Concluding remarks are given in Section 6.

##  2 Methods

The PK-4 experiment utilizes a long direct current (DC) discharge with an
active length of approximately 400 mm in a glass tube with inner diameter of
30 mm, equipped with both neon and argon gases (Pustylnik et al., 2016). The
experiment utilizes several tools for manipulation of the dust, including
movable radio frequency coils, a heating ring (thermal manipulator), an
auxiliary internal ring electrode (electrical manipulation), and a 20 W
continuous infrared laser (optical manipulation), which makes the system very
versatile. The DC drive is realized with a high voltage arbitrary waveform
generator with a frequency bandwidth up to 3 kHz, needed for applying polarity
switching to the electrodes. Six dust particle dispensers are available, each
filled with different mono-disperse spherical dust grains made of melamine-
formaldehyde (MF). In the experiment, the dust particles are suspended in the
center region of the discharge tube, in the bulk of the positive column. The
observation of the dust ensemble and discharge glow is realized by video
imaging, using a set of CCD cameras with an image resolution of 14.2 $\mu$m
per pixel (Schwabe et al., 2019). A detailed description of the setup and
early experiments can be found in Pustylnik et al. (2016).

Figure 1: (top) Schematic of the PK-4 experiment. Six microparticle dispensers
(D1-D6) are mounted on the sides. Cameras C1 and C2 each have a field of view
of 22.4 $\times$ 16.8 mm2 and can be moved along as well as across the plasma
chamber axis. (bottom) Dust particles within the PK-4 experiment showing the
formation of chains.

###  2.1 Gas discharge modeling

A cylindrical symmetric 2D Particle in cell with Monte Carlo collisions
(PIC/MCC) code was implemented and used to simulate the motion and collisions
of electrons and Ne+ ions in neon gas and at solid surfaces in a DC discharge
matching the PK-4 operating conditions. The electric field within the
discharge tube is determined self-consistently from the boundary conditions at
the electrodes and walls of the glass cylinder and the densities of the
charged species. The simulation was used to determine the plasma
characteristics within the PK-4 experiment for a DC plasma in neon held at a
pressure of $p=40$ Pa, gas temperature $T_{g}=300$ K, discharge current
$I=0.8$ mA (with approximately 1000 V DC voltage) with optional 500 Hz
polarity switching. A detailed description of the model, its implementation
and experimental verification are presented in a separate publication
(Hartmann et al., 2020).

Figure 2: Computed spatial distributions of plasma parameters: electron
density (a), Ne+ ion density (b), axial electric field (where positive
indicates in the direction of increasing $z$) (c), radial electric field (d),
mean electron energy (e), mean Ne+ ion energy (f) at $p=40$ Pa and $I=0.8$ mA
with the cathode at $z=0$. The data acquisition time was set to a very short
$0.25\,\mu$s. The real aspect ratio of 3:40 is scaled by stretching the radial
axis by a factor of two for better visibility.

Figure 2 shows the instantaneous spatial distribution of selected plasma
parameters. The global structure reproduces the traditional structure of long
DC discharges: a short cathode fall with large electric field, followed by a
low field region with even a reversed field feature, and the small field
positive column down to the anode. A dominant feature of the instant global
structure is the presence of ionization waves which develop on a $\mu$s-time
scale and travel along the column with phase velocities ranging between 500 m
s-1 and 1200 m s-1. These quasiperiodic waves are characterized by a large
amplitude modulation of the charged particle densities figure 2(a,b) and
alternating axial electric fields figure 2(c). A detailed analysis of the
global plasma parameters computed with the same simulation under similar
discharge conditions is presented in Hartmann et al. (2020). The time-averaged
plasma parameters in the central region are $n_{e}$ = $n_{i}$ = $2.1\times
10^{14}$ m-3, mean energies $\langle\epsilon\rangle_{e}=4.4$ eV and
$\langle\epsilon\rangle_{i}=0.04$ eV, and electric field $E=245$ V/m. The
presence of high amplitude ionization waves along the positive column makes
the time-dependence of the plasma parameters at a given position (where the
dust grains reside) of interest.

Here we focus on the local plasma environment in the central region of the
discharge at position $z=200$ mm and $r=0$. In the following graphs the time-
dependence of the plasma parameters is shown with 0.25 $\mu$s resolution
covering 250 $\mu$s total time at the central position of the cylinder. As
shown in figure 2 (a), the axial electric field varies in magnitude having a
small positive value between the ionization waves (about 100 V/m, where
positive indicates in the direction of increasing z) and peaking at about
-2000 V/m as an ionization front passes.

Figure 3: (a) Axial electric field at the center of the column. Drift velocity
of (b) electrons and (c) ions. The red shading indicates the times between the
ionization waves, and the regions shaded in green denote the times when the
electric field peaks within the ionization waves.

A similar structure is seen in the electron and ion velocities, which rapidly
increase in magnitude within an ionization wave. The velocities are measured
from the moments of the velocity distribution. The first moment is the average
velocity, which shows the net mean drift velocity $v_{d}$ imparted by the DC
electric field in the column (figure 3(b,c)). The second moment of the
velocity distribution gives the standard deviation, which is the average
(thermal) velocity of the plasma particles, $v_{th}$ (figure 4(a,b)). The
temperatures calculated from the time-dependent thermal velocities,

$T_{th}=\frac{2mv_{th}^{2}}{3k_{B}},$ (2)

are shown in figure 4 (c,d). The fully time-averaged electron and ion thermal
energies are $\langle\epsilon\rangle_{e}=4.4$ eV and
$\langle\epsilon\rangle_{i}=0.04$ eV. This is much greater than the average
energies calculated between the ionization waves (marked by the shaded
regions) $\langle\epsilon\rangle_{e}=3.4$ eV and
$\langle\epsilon\rangle_{i}=0.025~{}{\rm eV}=293$ K. In between the ionization
waves, the ions thermalize with the neutral gas at temperature $T_{n}=290$ K.

Note that the drift energy must be carefully taken into account in calculating
the mean thermal energy. According to Monte Carlo simulations of ion drift in
electric fields, the mean energy of the ions including the drift velocities is
given by (Robertson & Sternovsky, 2003)

$\frac{1}{2}m_{i}\langle
v_{i}^{2}\rangle=\frac{\pi}{4}m_{i}v_{d,i}^{2}+\frac{3}{2}k_{B}T_{n},$ (3)

where $T_{n}$ is the temperature of the neutral gas, leading to an expression
for the ion temperature as a function of the drift velocity (Trottenberg et
al., 2006)

$T_{dr,i}=T_{n}+(\frac{\pi-2}{6})\frac{1}{k_{B}}m_{i}v_{dr,i}^{2}.$ (4)

The ion temperature calculated in this manner is shown in figure 4(d) by the
red line. Applying Eq. 4 gives an average ion temperature of $T_{dr,i}$ = 380
K = 0.033 eV over the full time interval, greater than that between the
ionization waves, but less than that calculated without the drift correction.
Using an equation similar to Eq. (4) to calculate the average electron energy
shows that there is very little difference between the average electron energy
between the ionization waves and that averaged over the full time interval,
with $T_{dr,e}$ = 39543 K = 3.41 eV (as indicated by the red line in figure
4(c)).

Figure 4: (a,b) Thermal velocities for the electrons and ions in the axial
(blue) and radial (green) directions calculated from the standard deviation of
the velocity distribution. The velocities in the tangential direction (not
shown) are similar to those in the radial direction. (c,d) Temperature of the
electrons and ions calculated from the thermal velocities, Eq. (2) (blue
line), and the average temperature between ionization waves plus the drift
energy, Eq. (4) (red line). The shaded areas indicate the times between the
ionization waves when the ions thermalize with the neutral gas.

Since the plasma variations occur on the microsecond timescale and the dust
dynamics occur on the millisecond timescale, it seems reasonable to use the
time-averaged parameters to set the conditions used in the dust dynamics
model. However, the drift velocity plays an important role in determining
particle charge and the strength and extent of the ion wake. The ion drift
velocity in this case is less than the sound speed of the plasma
$c_{s}=\sqrt{k_{v}T_{e}/m_{i}}$. Given subsonic ion velocities, as the drift
velocity increases the ion current to a grain’s surface decreases, causing the
grain to become more negatively charged. An increased charge causes the ions
to be more strongly focused, resulting in a stronger ion wake. The increased
flow velocity also causes the spatial extent of the ion wake to be narrower in
the radial (cross-stream) direction and extended in the direction of ion flow
(Matthews et al., 2019). The interparticle interaction energy, as given by Eq.
1, also depends on the ion flow velocity, predicting that anisotropy in the
particle distribution begins to develop when $M_{th}>0.3$ (Ivlev et al., 2008,
2011). In between the striations, the average ion drift velocity is $v_{d,i}$
= 95 m/s = 0.22 $M_{th}$. The average drift velocity over all times is 165 m/s
= 0.39 $M_{th}$, which would seem to be just great enough to start to induce
anisotropy in the particle distribution. The average value within the
ionization waves (times noted by the green boxes in figure 2), is $\langle
v_{d,i}\rangle$ = 489 m/s = 1.14 $M_{th}$, with an average peak value of 1951
m/s = 4.05 $M_{th}$. Apparently, it during the ionization waves the ion flow
is great enough to cause a transition to strongly ordered strings.
Accordingly, we are interested in investigating the effect that the increased
electric field has on the formation of ordered dust strings in the PK-4
experiment.

###  2.2 Dust and ions simulation

The plasma conditions shown in Figs. 2 and 3 are used to model the dynamics
and charging of the dust in a flowing plasma using the molecular dynamics code
DRIAD (Dynamic Response of Ions and Dust) (Matthews et al., 2019), which
solves the equations of motion of the ions and dust on their individual time
scales. Here we compare the dust dynamics given the time-averaged plasma
conditions (Case 1) to three cases where the electron and ion temperatures are
set by the temperatures between the ionization waves (denoted by the red
shaded regions in Fig. 3), but the electric field is increased to yield
different values of the ion drift speed, $M_{th}=v_{dr,i}/v_{th}$. In Case 2,
the average axial electric field without the ionization waves present is used
(denoted by the red shaded regions in Figs. 3 and 4). In Case 3, the electric
field averaged over the ionization waves (as indicated by the green boxes in
Fig. 3) is applied. In Case 4, the magnitude of the electric field is set by
the average of the half-max of the electric field in the ionization waves. In
all cases, the polarity switching of the DC electric field is set to 500 Hz
with a 50% duty cycle (modeling symmetric switching of the electrode
polarities) and the average plasma density is set to $n_{e}=n_{i}=2.1\times
10^{14}$ m-3. The electron and ion temperatures, time-varying axial electric
field $\tilde{E}$, and resultant time-varying ion drift velocity
$\tilde{v}_{dr,i}$ for each case are given in Table 1.

Case | 1 | 2 | 3 | 4
---|---|---|---|---
$T_{e}$ (eV,K) | 3.41, 39500 | 3.38, 39200 | 3.38, 39200 | 3.38, 39200
$T_{i}$ (eV,K) | 0.033, 380 | 0.025, 290 | 0.025, 290 | 0.025, 290
$v_{th,i}(m/s)$ | 489 | 424 | 424 | 424
$\tilde{E}$ (V/m) | 245 | 100 | 510 | 1000
$\tilde{v}_{dr,i}$ (m/s) | 165 | 93 | 429 | 719
$M_{th}$ | 0.34 | 0.22 | 1.01 | 1.69
$\langle Q_{d}\rangle$ ($e^{-}$) | 3898 | 3667 | 4191 | 4819
$\Delta$ ($\mu$m) | 396 | 392 | 401 | 402
$\langle r\rangle$ ($\mu$m) | 14.5 | 12.6 | 11.6 | 11.9
$\langle r\rangle/\Delta(\%)$ | 3.6 | 3.2 | 2.9 | 3.0
Table 1: Discharge conditions used in the ion and dust simulation and
calculated dust charge, inter-particle spacing within the chain, and average
radial displacement.

##  3 Dynamics of Ions and Dust

In each case, we simulate the motion of 20 dust grains (melamine formaldehyde)
with radius $a=3.43~{}\mu$m, which corresponds to dust particle size available
in the PK-4 experiment. The dust particles are initially placed in a cloud
near the center of the simulation region, which has a radius of 1.5
$\lambda_{e}$ and length of 12 $\lambda_{e}$, where $\lambda_{e}=940~{}\mu$m
is the electron Debye length of the plasma calculated for Cases 2-4. The
equation of motion for the dust grains with mass $m_{d}$ and charge $Q_{d}$ is
given by

$m_{d}\frac{d\vec{v}_{d}}{dt}=\vec{F}_{dd}+\vec{F}_{id}+Q_{d}\tilde{E}+\nu^{2}Q_{d}r\hat{r}-\beta\vec{v}+\zeta(t).$
(5)

The forces between the dust particles $\vec{F}_{dd}$ are Coulomb interactions,
as the ions in the simulation provide the shielding, while the forces between
the dust and ions $\vec{F}_{id}$ are taken to be Yukawa interactions (Matthews
et al., 2019; Ashrafi et al., 2020). The ion-dust interactions are accumulated
over the elapsed ion timesteps and then averaged before calculating the dust
acceleration. The electric field $\tilde{E}$ is the axial electric field in
the DC plasma which switches direction with the polarity switching frequency.
There is a very strong confining force to keep the particles from the ends of
the simulation region where the ions are injected (the ions need to travel
approximately one Debye length to reach their equilibrium distribution). The
parabolic radial confinement potential approximates the electric field from
surrounding chains of charged dust particles where the confining strength
$\nu^{2}\propto\bar{Q}/(4\pi\epsilon_{0}\Delta^{3})$, $\bar{Q}$ and $\Delta$
are the average expected particle charge and particle separation, and a
constant of proportionality is used to account for the fact that there are
multiple chains providing the confinement. Depending on the number of nearest
neighbors assumed to participate in the confinement and the shielding length
of the interaction potential, this constant of proportionality can range from
$C=0.5-4.5$. Dust density wave experiments performed in the PK-4 in neon gas
at 40 Pa found an estimated particle charge of $Z_{d}\approx 2200$ for $a$ =
1.60 $\mu$m particles (Jaiswal et al., 2018); assuming the charge scales
linearly with the dust radius, the charge on a particle with radius
$a=3.43~{}\mu$m is estimated to be $Z_{d}\approx$ 4500\. The average
interparticle spacing, estimated from the number of particles visible in an
image frame from the PK-4 experiment, is $\Delta\approx$ 305 $\mu$m. In all
four cases simulated here, a fixed value of
$\nu^{2}=3.0\bar{Q}/(4\pi\epsilon_{0}\Delta^{3})=6.8\times 10^{5}$ Vm-2 was
used. The neutral gas (density $n_{g}$ and molecular mass $m_{g}$) provides
both an energy sink and source with the neutral gas drag depending on the drag
coefficient $\beta$ = $(4\pi/3)\delta a^{2}n_{g}m_{g}\sqrt{8k_{B}T_{g}/\pi
m_{g}}$ (where $\delta$ is a material-dependent constant in the range of 1.0 -
1.44; here we used 1.44 to represent diffuse reflection with accommodation of
gas molecules from a non-conductor) and a Langevin thermostat set by
$\zeta=\sqrt{2\beta k_{B}T_{g}/\Delta t_{d}}$ (the dust time step $\Delta
t_{d}$ = 0.1 ms). The system is allowed to evolve for 1.8 s, at which time the
dust particles have reached their equilibrium configuration.

The wakefield interactions are included self-consistently by solving the
equations of motion for the ions

$m_{d}\frac{d\vec{v}_{i}}{dt}=q_{i}\vec{E}+\vec{F}_{ii}+\vec{F}_{id},$ (6)

where the electric field consists of the confining electric field found within
a cylindrical cavity within a homogeneous distribution of background ions, as
well as the electric field in the DC plasma with polarity switching,
$\tilde{E}$. The ion-ion interactions $\vec{F}_{ii}$ are derived from a Yukawa
potential where the shielding is provided by the electrons, whereas the force
between the ions and dust $\vec{F}_{id}$ is taken to be Coulombic in nature.
This asymmetric treatment of the dust-ion forces has been shown to give a
reasonable quantitative agreement for the potential distribution and
interparticle forces (Piel, 2017). The ions reach equilibrium on a time scale
comparable to the ion plasma period
$2\pi/\omega_{i}=2\pi/\sqrt{n_{i}e^{2}/\epsilon_{0}m_{i}}=3.0\times 10^{-6}$
s, which is fast compared to the period of the polarity switching, 2 ms. The
effect of ion-neutral collisions are incorporated using the null collision
method (Donkó, 2011).

The charge on the dust grains is calculated self-consistently within the
plasma wakefield by summing the ion collisions over the elapsed ion timesteps
to determine the ion current. The electrons are assumed to have a Boltzmann
distribution and the electron current is set using orbital-motion-limited
(OML) theory.

##  4 Results

The resulting equilibrium dust charge and spatial configuration of the dust
are shown for the four cases in figure 5. The view shown is a projection into
the xz-plane, with the radial scale magnified to show the relative
displacement from the central axis. The ion-gas collisions cause the negative
charge of the particles in the chains (indicated by the marker color) to be
reduced from that predicted by OML theory, but the negative charge state
increases with the ion drift speed, as expected.

Figure 5: Final equilibrium charge and dust configuration for each case. Note
the scale in x is magnified to show the displacement from the central axis.
The color bar indicates the charge in units of elementary charge $e^{-}$. (a)
Case 1 $\langle Q_{d}\rangle$ = 3900 $e^{-}$, (b) Case 2 $\langle
Q_{d}\rangle$ = 3670 $e^{-}$, (c) Case 3 $\langle Q_{d}\rangle$ = 4190
$e^{-}$, (d) Case 4 $\langle Q_{d}\rangle$ = 4820 $e^{-}$.

The degree of order in the chain is evaluated using the linear pair
correlation function $g(r)$, which was calculated at each dust time step and
then averaged over the last 5000 time steps (0.5 s). The results are shown in
figure 6. In general, the order within the chain increases as the electric
field is increased (Cases 2-4). Case 2 (figure 6b) shows very little order
beyond the third peak. This is a clear indication that the enhanced wakes due
to the strong ion flow in the ionization waves contribute to the formation of
ordered chains. The fully time-averaged condition, Case 1, figure 6(a), leads
to a configuration which is more ordered than the thermal plasma without
ionization waves (Case 2), but less ordered than the other two cases.
Interestingly, the case with the highest degree of order is not that with the
greatest electric field and resultant ion flow, but Case 3, figure 6(c), which
employs the electric field averaged over the ionization waves.

Figure 6: Pair correlation functions averaged over 0.5 s for each case. (a)
Case 1, (b) Case 2, (c) Case 3, (d) Case 4.

Some clues to this order can be found by examining the ion density at
equilibrium and the overall electric potential of the system. In figure 7 and
figure 8, the ion density and the electric potential are shown for a slice in
the xz-plane. As shown in figure 7, each dust particle attracts a cloud of
ions. In Cases 1 and 2 with the averaged plasma conditions, a distinct ion
cloud surrounds each particle. As the electric field is increased in Cases
3-4, the ion cloud becomes elongated in the axial direction and the cloud
around a grain begins to merge with that of neighboring grains. The increased
particle charge, in addition to the increased ion flow speed, concentrates the
ions in a high-density ridge along the dust string.

Figure 7: Final equilibrium ion density, where the colorbar indicates the
density in units of the background density $n_{i}$/$n_{i0}$. The ion densities
are shown for a slice through the xz-plane averaged over 20 polarity cycles
(40 ms). (a) Case 1, (b) Case 2, (c) Case 3, (d) Case 4.

Finally, the combined electric potential from the ions and dust is shown at
equilibrium in figure 8. Note that these figures are zoomed in on the central
portion of the chain. The potentials are averaged over 20 polarity cycles
(0.04 s). The potential is measured with respect to the maximum potential just
upstream/downstream of the dust string at $z\approx\pm$ 4 mm. Profiles of the
total potential along the axial direction are compared in figure 9 just above
the dust string (in the radial direction) at $x=0.2$ mm (figure 9a) and along
the center of the dust chain at $x=0.0$ mm (figure 9b). Note that in Cases 1
and 2 the overall potential is dominated by the dust grains and is negative
over much of the region surrounding the string. In Case 3, the potential is
slightly positive just to the outside of the dust chain. In Case 4, an
alternating positive/negative potential structure starts to emerge along the
length of the chain.

Figure 8: Equilibrium electric potential, where the colorbar indicates the
difference from the maximum positive potential upstream/downstream of the
strings in mV. The potentials are shown for a slice through the xz-plane
averaged over 20 polarity cycles (40 ms). (a) Case 1, (b) Case 2, (c) Case 3,
(d) Case 4.  Figure 9: Equilibrium electric potential along the axial
direction averaged over 20 polarity cycles (40 ms). In (a), the profile is
shown just outside the dust string along $x=0.2$ mm, in (b) the profile is
shown along the center of the dust string at $x=0.0$ mm. The maximum positive
potential between the dust grains are marked with symbols for each of the four
cases.

##  5 Discussion

It is expected that the radial confinement should be proportional to
$Q_{d}^{2}$, assuming that the radial confinement is due to the interaction
between neighboring strings. As given in Eq. 5, the magnitude of the radial
confining force is $\nu^{2}Q_{d}r$. For simplicity, the constant $\nu^{2}$ was
set to be $6.8\times 10^{5}$ Vm-2 for all of the cases, resulting in a
restoring force which is proportional to $Q_{d}$. Thus the radial restoring
force used can be considered to be underpredicted for Case 3 and 4 and
overpredicted for Case 2, relative to Case 1. The average radial position of
all the particles in each chain as a function of time is shown in figure 10.
After the initial Coulomb expansion of the dust cloud at the beginning of the
simulation, the particles all settle near the z-axis. As expected, the case
with the largest average particle charge (Case 4) experiences the greatest
radial restoring force and reaches the equilibrium radial position most
quickly, followed by the other cases in order of decreasing average particle
charge. However, even though the particles in Cases 3 and 4 have the greatest
average charge, these chains have the smallest average radial displacement,
representing better string structure. Notably, Case 1, with the time-averaged
plasma conditions, has the greatest average radial displacement. This is a
clear indication that the ion focusing produced by the strong axial electric
field in Cases 3 and 4 allows for a smaller inter-particle spacing within the
string, despite the increased particle charge, and enhances string alignment.

Figure 10: Average radial displacement of particles in the numerical
simulation. The dashed lines indicate the average radial displacement over the
last 0.6 s, after all of the particles have reached their equilibrium
configuration. At equilibrium, the average radial displacements are 14.5
$\mu$m, 12.6 $\mu$m, 11.6 $\mu$m, and 11.9 $\mu$m for cases 1-4, respectively.

For comparison, data from Campaign 4 of the PK4 experiment performed in
February, 2017, is shown in figure 11a showing chains consisting of 6.86
$\mu$m-diameter particles which were observed in neon gas at 45 Pa. The
particles were trapped by the polarity-switched discharge (current 1.0 mA and
frequency 500 Hz) with a duty cycle of 0.72, in order to compensate for the
residual gas flow. A duty cycle of 0.72 corresponds to an asymmetric AC mode
with 72% of the cycle at positive voltage and 28% at negative voltage. The
linear pair correlation function for five different chains (marked by the
different symbols), were calculated and averaged over 70 frames (1.0 s) as
shown in figure 11b. Qualitatively, the pair correlation functions most
closely resemble that shown for Case 3 (figure 6c) in that there are distinct,
separate peaks out to the position of the sixth-nearest neighbor. The average
inter-particle spacing for the five chains is
$\Delta=270,282,281,270,277~{}\mu$m, from top to bottom, respectively,
calculated from the first peak in g(r). The average radial displacements of a
chain’s particles, measured as the perpendicular distance from a linear fit to
the positions of the particles in a chain are $\langle
r\rangle=11.6,20.4,16.8,13.2,17.8~{}\mu$m. In the experiment, the average
inter-particle spacing within the chain is smaller, and average radial
displacement is larger, than that found for the four cases in the numerical
model (see Table 1), such that $\langle r\rangle/\Delta$ = 4.3, 7.2, 6.0, 4.9,
6.4% for each chain, respectively. This suggests that the particle charge in
the experiment may be less than estimated, possibly due to the fact that the
dust density is great enough to deplete the electrons in the vicinity of the
dust cloud. This would result in stronger ion wake potentials along the chain
axis and weaker repulsion between neighboring chains, allowing the particles
more freedom for radial displacements. Another possible explanation for the
observed larger average radial displacement of the dust particles in the
experiment, as compared to the simulation, is that the asymmetric duty cycle
used in the experiment lead to asymmetric ion focusing around the dust grains.
This could produce a stronger positive wake on one side of the dust, allowing
smaller intra-chain particle spacing, while weakening the radial restoring
force and resulting in less stable chains.

Figure 11: (a) Chains of dust particles observed in the PK-4 experiment.
Symbols mark particles in five different chains which remained intact over the
full time period. (b) Linear pair correlation function for each chain marked
in (a), averaged over 70 frames (1.0 s). Each line is successively offset by
2.5 for clarity.

##  6 Conclusion

A simulation of dust dynamics within a DC discharge plasma was used to
investigate the role of strong electric fields created by ionization waves on
the formation of chain-like dust structures within the plasma. A PIC/MCC code
was used to determine the plasma conditions within the discharge tube, which
were used to set the initial conditions and boundary conditions for an N-body
simulation resolving the motion of the ions and the dust. The PIC/MCC
simulation revealed that there are very strong variations in the plasma
conditions on the microsecond scale which result in a large axial electric
field with a peak magnitude of about 2000 V/m, about 20 times greater than the
background value between the ionization waves. Simulations of dust charging
and dynamics show that time-averaged plasma temperatures and axial electric
field lead to a weakly ordered string structure, leading to the conclusion
that the time-averaged conditions don’t seem to fully capture the plasma
conditions which lead to chain formation. However, simulations using the
plasma temperatures and densities between the ionization waves with an applied
axial electric field show that the order within the string increases with the
electric field strength. The numerical results most closely resemble data from
the PK-4 experiment when the average electric field during the ionization
waves is applied. It appears that the enhanced electric field associated with
the ionization waves could play an important role in generating the string-
like structures observed in the PK-4 experiment.

These simulations were run assuming constant plasma conditions including
electron and ion temperatures and number densities. Future work will examine
the effect of the time-varying plasma parameters calculated from the PIC/MCC
simulation on the dust charging and dynamics.

All authors gratefully acknowledge the joint ESA – Roscosmos “Experiment
Plasmakristall-4” on-board the International Space Station. The microgravity
research is funded by the space administration of the Deutsches Zentrum für
Luft- und Raumfahrt e.V. with funds from the federal ministry for economy and
technology according to a resolution of the Deutscher Bundestag under Grants
No. 50WM1441 and No. 50WM2044. A. M. Lipaev and A. D. Usachev were supported
by the Russian Science Foundation Grant No. 20-12-00365 and participated in
preparation of this experiment and its execution on board the ISS. L. S.
Matthews, T.W. Hyde and M. Rosenberg received support from NASA Grant number
1571701 and NSF Grant numbers 1740203 (LSM, TWH, and MR) and the US Department
of Energy, Office of Science, Office of Fusion Energy Sciences under award
number DE-SC-0021334 (LSM and TWH). P. Hartmann gratefully acknowledges
support from the Hungarian Research, Development and Innovation Office via
grant K-134462.

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